Geometry; 12/19

We spent a little time at the beginning of the period reviewing the distance formula, circle equation, and slope equations that we have worked with the past 3 days.  We then went over and turned in the homework.  The students took the rest of the period taking the chapter 13 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 12/19

The students turned in their chapter 6 review materials at the beginning of the period.  They then spent the period taking the chapter 6 test.


Assignment:  none;  extra credit puzzle option

Geometry; 12/18

We continued our work with chapter 13 today by taking a look at how to use slope to determine if lines are parallel or perpendicular.  Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.  These algebra concepts are ones that we then used to evaluate various figures that we graphed using points that were supplied.  We went through a couple of examples together before getting started on the homework.


Assignment:  section 13-3;  page 536;  CE #1-9;   page 537;  WE  #1-3, 5, 6, 9-11, 13

Honors Geometry; 12/18

We spent some time going over the review from Friday and answering questions that the students had.  We also went through 2 more inequality proofs together before getting started on the 2nd of our reviews in getting ready for the chapter 6 test.


Assignment:  Chapter 6 Review  #2

Ch. 6 Test tomorrow


Test 24 ;  Chapter 6 Test

1.  false
2.  true
3.  true
4.  false
5.  true
6.  a.  If pts. X, Y, and Z are noncollinear, then XY + YZ does not equal XZ
     b.  If XY + YZ does not equal XZ, then pts. X, Y, and Z are noncollinear.
     c.  XY + YZ does not equal XZ
7.  less than
8.  greater than
9.  greater than
10.  equal
11.  less than
12.  less than,  greater than
13.  greater than
14.  equal
15.  greater than
16.  angle L
17.  segment NO
18.     a.  HF
          b.  SAS inequality theorem
19.  a.  FG
       b.  Longer side is opposite the larger angle  (triangle inequality theorem)
20.  a.  HF
       b.  longer side is opposite the larger angle  (triangle inequality theorem)

21.          statements                                    reasons
           angle 1 > angle DBC                   ext. angle is greater than either remote int. angle
           DC congruent to BC                    given
           angle BDC cong. angle DBC      isos. triangle theorem
           angle 1 > angle BDC                  substitution



Inequality Proofs

1.  statements                                            reasons
angle C > angle A                         given
angle D > angle B                         given
AE > CE                                       longer side is opposite larger angle in triangles
BE > DE                                       longer side is opposite larger angle in triangles
AE + EB = AB                             segment addition postulate
CE + ED = CD                             segment addition postulate
AB > CD                                      property of inequality


2.    don't do this proof

3. statements                                          reasons
angle 1 less than angle 3               given
BA parallel to CD                         given
AC > AD                                      given
angle 3 congruent angle 2             if lines parallel, then AIA congruent
angle 1 < angle 2                          substitution
BC > AC                                       longer side is opposite larger angle in triangle
BC > AD                                       subst. /  transitive


4.  statements                                        reasons
AC bisects angle BAD                   given
angle 1 congruent to angle 2          def. of bisect
angle 3 = angle B + angle 1           ext. angle = sum of remote int. angles
angle 3 > angle 1                            property of inequality
angle 3 > angle 2                            substitution
AD > CD                                        longest side is opposite largest angle in triangle

Geometry; 12/15

We had shortened periods today due to our winter assembly, so our lesson focused on a brief review of how to determine the slopes of lines.  This algebra topic will be used quite a bit as we move through chapter 13.


Assignment:  page 532-533;  section 13-2;  WE 1-21 all

Honors Geometry; 12/15

We spent some more time today working on how to work with inequalities in triangles.  We went through a few drawings together that involved setting up algebra inequalities that then need to be solved.  The students then got started working on their chapter 6 review.

Assignment:  Chapter 6 review

Geometry; 12/14

We started a new chapter today -- coordinate geometry.  We are skipping ahead to chapter 13 and we will return to pick up the other chapters during the next semester.

Our topic today was how to use the distance formula in working with straight sided figures and circles.  We used the pythagorean theorem to find the distance formula, and then we also showed how the formula of a circle can be found.  We practiced with both types of problems before getting started on the assignment.


Assignment:  section 13-1;  page 526-527;  WE 5-12;  17-25

Honors Geometry; 12/14

Our work with inequalities focused on two different triangles today.  The inequality theorems between two triangles are known as the Hinge Theorems.  We showed how these two theorems work and how to use them to solve various types of drawing examples.


Assignment:  section 6-5;  page 230;  CE 1-8;  page 231-232;  WE 1-11

Geometry; 12/13

The students turned in their chapter 5 review materials and entry tasks to start the period today.  The remainder of the period was spent taking the chapter 5 test.


Assignment:  none;  extra credit puzzle

Honors Geometry; 12/13

Our topic for today involved working with inequalities in one triangle.  We went through the triangle inequality theorems to show how the range of side lengths can be determined in a triangle, as well as how to make comparisons between angles and sides in a single triangle.  The concept is fairly simple -- the longest side is always opposite the largest angle;  the shortest side is always opposite the smallest angle.  The students then got started on their homework assignment.

Assignment:  section 6-4;  page 222-223;  WE 10-16, 19

     Inequalities in 1 Triangle worksheet

Geometry; 12/12

We completed our quadrilaterals chart today by filling in the properties of kites that we had worked with yesterday.  We then worked through 2 problem types for the test together before getting started on the review sheet.  The students had the last half of the period to work on the chapter 5 review.  The chapter 5 test is tomorrow.


Assignment:  Chapter 5 Review sheet


Ch. 5 Practice

1.  true
2.  false
3.  false
4.  true
5.  false
6.  angle Q
7.  RQ
8.  7.5
9.  3.7
10.  trapezoid
11.  6
12.  x = 3;  DF = 18
13.  92,  88
14.  rectangle
15.  angle WXY congruent to angle WZY
16.  WX parallel to ZY  or WZ congruent to XY
17.  WX parallel to ZY  or WZ congruent to XY
18.  ZP congruent to PX

19.    statements                                               reasons
      XZ  segment                                         auxiliary line
      XZ congruent to XZ                             reflexive
     angle 1 congruent to angle 2                 if lines parallel, AIA congruent
     tri. WXZ cong. tri. YZX                       AAS
     WX congruent to ZY                            CPCTC
     WXYZ is parallelogram                       if one pair of sides both cong. and parallel,
                                                                   then it is a parallelogram

Quadrilaterals

1.  92, 88
2.  10
3.  2
4.  3
5.  13.4
6.  90
7.  angle HEF congruent to angle HGF
8.  EF parallel to HG   or EH congruent to FG
9.  EF parallel to HG   or EH congruent to FG
10.  I is the midpoint of HF
11.  A, 13
12.  24
13.  trapezoid
14.  median / midsegment
15.  isosceles trapezoid
16.  18
17.  80, 80
18.  rectangle
19.  rhombus
20.  isosceles trapezoid

Trapezoids

1.  16
2.  17
3.  9
4.  8
5.  2
6.  78
7.  63, 117
8.  72, 108
9.  13
10.  15
11.  65, 115, 115
12.  angle B,  angle CFE, angle DEF
13.  10, 15
14.  6, 18
15.  12
16.  24, 12
17.  JK = 2x;  x = 1.2

Honors Geometry; 12/12

We continued our work with inequalities in geometry today by taking a look at what the phrases are that are used with inequalities.  We learned how to write inverses and contrapositives in our lesson today, and went over how to make conclusions from these different types of statements.  We also demonstrated how to illustrate an inequality problem with a venn diagram.

Assignment:  Section 6-2;  pg. 210-212;  WE 1-18

Geometry; 12/11

We reviewed the various properties of trapezoids today before taking a look at the last quadrilateral we will study --- kites.  We went over the 2-3 properties of kites and then how to use these properties in calculations.  The students spent the last part of the period working on their assignment.


Assignment:  Kites worksheet

Honors Geometry; 12/11

We began our shortest chapter of the year today --- inequality in geometry.  We introduced the concepts of how to use drawings and some of the foundational postulates of geometry to create inequality statements between figures.  We went over 3-4 examples before getting started on the homework.

Assignment:  section 6-1;  page 205;  CE #1-19 all;  page 206-207;  WE #1-8 all

Geometry; 12/8

We continued our work with quadrilaterals today by going over the properties of trapezoids.  We went through the calculations involving trapezoids and how to work with the midsegment theorem.  We also showed what an isosceles trapezoid is and how its properties can be used to solve various types of calculation problems.

Assignment:  Trapezoids worksheet

Honors Geometry; 12/8

The students got their chapter 5 tests back today and were able to ask any questions that they had.  We spent today doing two things:   One was to introduce the geometry scavenger hunt project and the other was to review the concept of working with quadratics.  The project is due after Christmas break, and the quadratics is an algebra skill that needs to be mastered before working with more of the questions that are coming up in the future chapters. 


Assignment:  algebra review:  page 163;  #1-33;  skip every 3rd problem

Geometry; 12/7

We continued our work with special parallelograms today by taking a look at how to work through calculations with rectangles, rhombi, and squares.  We went through 4-5 examples together, as well as demonstrating again how to use the pythagorean theorem to work with right triangles.  The students then got started on their homework assignment.


Assignment:  special parallelograms worksheet +  page 187;  WE  #11-19

Honors Geometry; 12/7

After turning in the entry tasks and the reviews for chapter 5, the students took the period today to complete the chapter 5 test.


Assignment:  none;  extra credit puzzle option

Geometry; 12/6

The first part of today was spent explaining the geometry scavenger hunt project.  This project involves finding pictures of a wide variety of geometric figures in real life objects.  There is a written explanation for this project as well that was handed out.  The rest of the period was spent covering the different properties of special parallelograms.  We went over the rectangle, the rhombus, and the square in the lesson today. 

Assignment:  page 186;  CE #1-7;    page 187;  WE #1-10

Honors Geometry; 12/6

We answered several questions about the kites homework last night before getting started with our review for the chapter 5 test tomorrow.  We worked through 4 different problem types with partners to illustrate the different concepts from the chapter.  After the partner activity, the students then got started on their review assignment.


Assignment:  Chapter 5 Review assignment



Trapezoid and Kite Properties Review Sheet

1.  115
2.  88
3.  angle F = 60;  angle D = 120;  angle E = 120;  EF = 15
4.  bases:  YV and XW
     angle V = 70;  angle W = 110;  angle X = 110
5.  x = 124,  y = 56
6.  BC = 12;  DC = 4;  perimeter = 32
7.  a = 134
8.  JL = 22
9.  EG = 8.7
10.  x = 30
11.  x = 45;  y = 30;  w = 120
12.  x = 10;  y = 40
13.  x = 30;  y = 60;  z = 8.06
14.  x = 64;  y = 43

Geometry; 12/5

We turned in the chapter 5 quiz reviews to begin the period today.  The main task in class today was to take the chapter 5 quiz.

Assignment:  none;  extra credit puzzle option

Honors Geometry; 12/5

We covered our last quadrilateral today -- kites!  These shapes have 3 unique properties that we used to solve various types of problems and to complete our quadrilaterals chart.  We went over 3-4 calculation examples together before getting started on the homework.


Assignment:  Kites worksheet

Geometry; 12/4

We spent time in class today reviewing parallelogram proofs, parallelogram calculations, and working with systems of equations.  All three of these topics will be involved on the chapter 5 quiz tomorrow.


Assignment:  Chapter 5 Quiz review

Review Sheet Answers

1.  14
2.  20
3.  34
4.  24
5.  17
6.  12
7.  105
8.  75
9.  75
10.  26
11.  121
12.  59
13.  121
14.  49
15.  59
16.  33
17.  26
18.  72
19.  105
20.  68

21.    both pair of opposite sides are parallel
         both pair of opposite sides are congruent
         both pair of opposite angles are congruent
         both pair of SSI angles are supplemental
         both diagonals bisect
         one pair of sides is both congruent and parallel

Proof:

      Statements                                               Reasons
ABCD is a parallelogram                                given
DC congruent to AB                                   if parallelogram, opp. sides congruent
DO congruent to BO                                   if parallelogram, diagonals bisect
CO congruent to AO                                   if parallelogram, diagonals bisect
triangle DCO congruent to tri. BAO           SSS

vertical angles could also be used;  AIA could also be used

Ways to Prove that Quadrilaterals are Parallelograms

1.  14
2.  24
3.  53
4.  50
5.  6
6.  14
7.  20
8.  25
9.  43
10.  both pairs of opp. sides are congruent
11.  one pair of opp. sides is both parallel and congruent
12.  both pair of opp. sides are parallel
13.  diagonals bisect
14.  both pairs of opp. angles are congruent

15.  Proof.

1.  given
2.  CPCTC
3.  def. of midpoint
4.  def. of bisector
5.  if diagonals bisect, then PART is a parallelogram

Page 182;  #7

See answer in back of book

Honors Geometry; 12/4

We went through another shape today in our study of quadrilateral --- the trapezoid.  This shape only has 1 pair of opposite sides that are parallel, so the properties that it possesses are quite different from those of the parallelograms we have been working with.  We demonstrated what the midsegment of a trapezoid looks like and how to calculate it using the two bases.  We also went through the unique properties of an isosceles trapezoid.


Assignment:  section 5-5;  page 192-193;  WE #1-25 all

Geometry; 12/1

We spent time today reviewing the various concepts of the first part of the chapter by going over 4 different types of problems with a partner.  The students worked with a variety of drawings and calculations during the period before getting started on their assignment at the end of period.

Assignment:  Midsegments worksheet

Honors Geometry; 12/1

We continued our work with special parallelograms today, focusing on the calculation shortcuts using rhombi, rectangles, and squares.  We also demonstrated one proof that involved a rhombus to show how to use its properties.


Assignment:  section 5-4;  page 187-188;  WE  #11-28, 30

Geometry; 11/30

Our topic today focused on three different theorems involving parallel lines.  Each one involved a particular type of drawing and then learning how to use the concept to work with some mental math problems.  We went through a few examples together before getting started on the assignment.


Assignment:  section 5-3;  page 180-181;  WE 1-17 all;  page 182;  Self Test 1;  #1-6

Honors Geometry; 11/30

Our topic today was looking at various properties of special types of parallelograms.  We began building an overall chart of quadrilaterals and added rectangles, rhombi, and squares to the mix of what we are studying.  Each one has some unique properties that can aid in solving problems.  We went through a few examples together of each before the students got started on their assignment.


Assignment:  section 5-4;  page 186-187;  CE 1-10, WE 1-10;  Page 182;  Self Test 1:  #1-7

Geometry; 11/29

We continued our work with parallelograms today by taking a look at how to work with parallelogram proofs.  These types of proofs rely heavily on congruent triangle proofs, so there are just a few properties of parallelograms to work in.  We went through 3 together before the students got started on their assignment.


Assignment:  parallelogram calculations worksheet + page 169-170;  WE 29, 32

Honors Geometry; 11/29

After turning in our review materials, the students took the chapter 5 quiz in class today.


Assignment:  none;  extra credit puzzle option

Geometry; 11/28

We continued our work with parallelogram properties today, adding a 6th property to the 5 that we introduced yesterday.  We showed how to use these six properties to recognize whether or not figures are parallelograms.  We went through 5-6 drawings together before getting started on the assignment.

Assignment:  proving parallelograms worksheet +  page 173;  CE #1-9 all

Honors Geometry; 11/28

We went over our chapter 5 quiz review together in class, answering any questions the students had.  We then went through a review exercise in which partners worked with several different types of review problems in 5 minute intervals.  After 4 of these rotations, the students then got started on their second quiz review towards the end of the period.


Assignment:  Chapter 5 Quiz review #2



Lesson 5-1 practice worksheet

1.  both pairs of opposite angles congruent in parallelograms
2.  diagonals bisect in parallelograms
3.  both pairs of opposite sides congruent in parallelograms
4.  both pairs of opposite sides congruent in parallelograms

5.  WX = 15
6.  angle WXY = 110
7.  XP = 13
8.  WY = 36
9.  angle WXY = 105
10.  angle WZY = 120

11.  angle STP = 112
12.  angle PSR = 100
13.  angle PQR = 100
14.  angle PSQ = 25

15  QR = 19
16.  RS = 25
17.  x = 6
18.  angle P = 105
19.  x = 16
20.  x = 7

Two column proof

Statements                                                     Reasons
ABCD is parallelogram                                 given
P is midpoint of AB                                       given
Q is midpoint of DC                                      given
AP parallel to DQ                                          opp. sides of large parallelogram parallel
AP = 1/2 AB                                                  midpoint theorem
DQ = 1/2 DC                                                 midpoint theorem
AB = DC                                                       opp. sides of large parallelgram congruent
AP = DQ                                                       transitive
AP congruent DQ                                         def. of congruent
APDQ is parallelogram                                if one pair of sides is both parallel and
                                                                      congruent, then figure is parallelogram

Lesson 5-2 Practice worksheet

1.  yes;  both pairs of opposite sides are congruent
2.  yes;  both pairs of opposite sides are parallel
3.  yes;  one pair of opposite sides are both congruent and parallel
4.  no conclusion possible
5.  yes;  diagonals bisect each other
6.  yes;  both pairs of opposite sides are congruent
7.  yes;  both pairs of opposite angles are congruent

Geometry; 11/27

The students got back their chapter 4 test today and were able to ask questions if they had them on the test.  We then got started with our next unit today by introducing the topic of parallelograms.  We went over 5 properties of parallelograms and how to use them in solving various calculation problems. 

Assignment:  section 5-1;  page 169-170;  WE 1-12 all;  17-26 all

Honors Geometry; 11/27

We continued with our work on parallelograms today by going over 2 more parallelogram proofs together in class.  The students then started working on their assignment to carry out a few more proofs on their own, as well as reviewing some of the calculations we studied last week. 


Assignment:  Parallelogram Proof Packet

Geometry; 11/22

We spent the short period today working on a series of toothpick geometry puzzles to see how many the students could figure out in the 20 minutes we had. 


Assignment:  none;  Happy Thanksgiving!

Honors Geometry; 11/22

We went over the homework and took any questions that the students asked to start off the period.  The rest of the short period was spent working on a series of toothpick geometry puzzles to see how many the students could figure out in the 20 minutes we had. 


Assignment:  none;  Happy Thanksgiving!

Geometry; 11/21

The students turned in their reviews and entry tasks at the beginning of the period.  The majority of the period was then spent taking the Chapter 4 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 11/21

We continued our work in chapter 5 today by taking a look at various theorems involving parallel lines.  We went over what a midsegment is, and what properties it possesses when dealing with triangles and parallel lines.  We also worked with some diagrams that had multiple parallel lines and transversals.


Assignment:  section 5-3;   page 180-181;  WE 1-19 all

Geometry; 11/20

We spent today reviewing the different problem types that will be on the chapter 4 test tomorrow.  We went over 4 different partner problems together before the students got started working on their review sheet.

Assignment:  Chapter 4 Review

Ch. 4 Test tomorrow

Review Sheet Answers

Test 14 answer key

1.  segment SY
2.  angle Q
3.  triangle SQY
4.  a.  none     b.  none
5.  a.  triangle QRP congruent to triangle SRT    b.  SAS
6.  a.  triangle KLJ congruent to triangle NLM    b.  ASA
7.  a.  triangle ABC congruent to triangle DEC    b.  SAS
8.  a.  triangle FIG congruent to triangle HIG      b.  ASA
9.  a.  triangle OQR congruent to triangle QRP    b.  SSS
10. a.  none    b.  none
11.  after
12.  after
13.  before
14.  before
15.  before
16.  after
17.  after
18.  after


Test 15 answer key

1.  a.  segment QR       b.  segments PQ and PR
2.   a.  angle Y or angle Z
      b.  segment YZ
      c.  angle X
      d.  segment XY or segment XZ
3.  angle A,  angle 1
4.  angle 3,  angle C
5.  segment AB,  segment DB
6.  segment DC, segment BC
7.  7
8.  37.5
9.  a.  triangle ABC congruent to triangle DEC
     b.  HL
10.  a.  none     b.  none
11.  a.  triangle JKL congruent to triangle NML    b.  AAS
12.  a.  triangle PQR congruent to triangle PSR    b.  ASA

13.  Proof

      statements                                                                 reasons
AB parallel to DE;  angle B congruent to angle D          given
angle 1 congruent to angle 4                                           if lines parallel, then AIA congruent
AC congruent to AC                                                       reflexive
Tri. ABC congruent to Tri. CDA                                   AAS
AD congruent to BC                                                       CPCTC

Honors Geometry; 11/20

We continued our study of parallelograms by taking a look at how to prove that figures are parallelograms.  We went through some recognition drawings together, as well as working through a two - column proof that involved proving a parallelogram.  The students then got started on their assignment.


Assignment:  section 5-2;  page 173;  CE 1-9;  page 175;  WE 14-16, 19-22;  page 170,  WE 32

Geometry; 11/17

We wrapped up chapter 7 today by taking a look at 3 different figures that are involved with triangles -- medians, altitudes, and bisectors of sides and angles.  We demonstrated how to draw each of these figures and saw how each triangle has 3 each of them---all intersecting in a common point.  We practiced each drawing together before getting started on the assignment.


Assignment:  section 4-7;  page 155;  CE #1-7;  page 156;  WE #1-4;    4-5/4-6 worksheet

Honors Geometry; 11/17

The students got their chapter 4 test back today and had a chance to go over any mistakes they had made.  We then got started on our next topic of study -- quadrilaterals.  We went over 5 different properties of parallelograms together, showing how congruent triangles and parallel lines can be used to take all kinds of shortcuts with parallelogram calculations.

Assignment:  section 5-1;  page 169-170;  WE 1-12;  16-28

Geometry; 11/16

We continued our study of congruent triangles by taking a look at how two sets of congruent triangles can be used to prove things.  We went through a couple of examples together and then demonstrated a shortened version of a proof called a key step proof.

Assignment:  Section 4-6;  page 148-149;  WE #1-9

Honors Geometry; 11/16

The students turned in their chapter 4 review materials today before taking the chapter 4 test.  They had the period to finish the test.


Assignment:  Chapter 4 Test;  extra credit puzzle option

Geometry; 11/15

We continued to work with the different methods of proving triangles congruent today by taking a look at some drawings that involve overlapping triangles.  We demonstrated how both sides and angles can overlap, and that these need to be determined before the proof can be completed.  After a couple of examples, the students then got to work on a proof worksheet that involves all 5 methods of proving triangles congruent.


Assignment:  CPCTC Triangle Proof worksheet

Honors Geometry; 11/15

We spent some time going over the chapter 4 review sheet to begin class.   We then went over one proof together from the proof packet to illustrate one more overlapping triangle proof.  The rest of the time the students had to work on finishing their proof packet and the 2nd review sheet for chapter 4.

Chapter 4 Test is tomorrow.

Assignment:  Chapter 4 Review #2

Review Sheet #2 answers

Test 15

1.  3
2.  163
3.  145
4.  triangle SNA congruent to triangle KAN;  AAS
5.  triangle SNE congruent to triangle KAE;  ASA
6.  none
7.  triangle SNA congruent to triangle KAN;  HL thm
8.  triangle SEN congruent to triangle KEA;  SAS
9.  none
10.  triangle SEN congruent to triangle KEA;  ASA
11.  132
12.  x = 10;  angle A = 96
13.            statements                                   reasons
      EP perp. SK                                         given
      SD perp. EK                                        given
      angle SPE and angle EOS rt. angle     def. of perpendicular
      angle SPE congruent to angle EOC    all rt. angles congruent
      SK congruent EK                                given
      angle PSE congr. angle DES               if isos. triangle, base angles congr.
      SE congr. SE                                       reflexive
      triangle SEP congr. to triangle ESD   AAS

Test 16

1.  false
2.  true
3.  false
4.  true
5.  true
6.  true
7.  yes
8.  no
9.  no
10.  drawings on diagram
11.  SR, ST
12.    a.  SSS
         b.  CPCTC
         c.  triangle SXP cong. to tri. SXT;  SAS
         d.  CPCTC
         e.  def. of midpoint
         f.  def. of median

Geometry; 11/14

We introduced two new methods for working with congruent triangles today---the AAS method and the HL Thm method.  Both of these involve using previous theorems from geometry and they are used just like the first three triangle methods.  We introduced the concept of overlapping triangles today as well.


Assignment:  section 4-5;  page 142;  CE 1-11;  page 143-144;  WE 1-7

Honors Geometry; 11/14

We continued our work with the vocab words "altitude", "median", and "perpendicular bisector" today by showing how these concepts are used in triangle proofs.  We also answered some other review questions together before getting started on the review sheet for the chapter 4 test.


Assignment:  Chapter 4 Test Review #1

Geometry; 11/13

We continued our study of triangles today by taking a look at some of the properties of isosceles triangles.  We went over how to use base angles and the perpendicular bisectors of the base to find shortcuts to calculations.  The key ingredient was that the triangle had to be isosceles (2 sides congruent).  We went over 3-4 examples together before getting started on the homework assignment.


Assignment:  section 4-4;  page 137;  WE 1-10, 13;  +  Isosceles Triangle worksheet

Honors Geometry; 11/13

We spent some time at the beginning of the period going over a couple of proofs from the proof collection.  We then went through a lesson on medians, altitudes, and bisectors today in class.  The lesson largely focused on identifying these vocab terms in various types of drawings.  We introduced each term together before getting started on the assignment.


Assignment:  section 4-7;  page 155, CE 1-7;  page 156-157;  WE 1-13, 20

Geometry; 11/9

The students turned in their chapter 4 quiz reviews to start the period today before taking the rest of the period to work on the chapter 4 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 11/9

The students spent the period today working on a collection of triangle proofs that helps review the entire chapter.  This packet will be due on Wednesday of next week.


Assignment:  Congruent Triangles Packet

Geometry; 11/8

We practiced a couple more triangle proofs involving vocabulary words.  We also went over a couple of examples of "before and after" problems involving triangles.  The rest of the period was spent working on the chapter 4 quiz review sheet.

Chapter 4 quiz is tomorrow:

Assignment:  Chapter 4 quiz review


Some Ways to Prove Triangles Congruent

1.  angle U
2.  m of angle D
3.  segment SU
4.  segment UN
5.  triangle NSU
6.  triangle EDR
7.  triangle FAN
8.  angle D;  CPCTC
9.  segment BA;  segment BF
10.  SAS
11.  ASA
12.  none
13.  none
14.  SSS
15.  ASA
16.     1.  given      2.  vertical angle congruent     3.  SAS

Using Congruent Triangles

1.      1.  given
         2.  vertical angles congruent
         3.  SAS
         4.  CPCTC

2.     1.  given
        2.  if lines parallel, then corr. angles congruent
        3.  ASA
        4.  CPCTC
        5.  if corr. angles congruent, then lines parallel


3.  1.  given
     2.  def. of midpoint
     3.  reflexive
     4.  SSS
     5.  CPCTC
     6.  def. of angle bisector


Practice 14

1.  segment OP
2.  BI
3.  angle O
4.  m angle G
5.  triangle OTP
6.  triangle IGB
7.  sometimes
8.  always
9.  never
10.  SAS
11.  ASA
12.  none
13.  ASA
14.  none
15.  SAS

16.         statements                                     reasons
        M is midpoint of XY                      given
        XM congruent YM                        def. of midpoint
        XZ congruent YZ                          given
        ZM congruent ZM                         reflexive
       triangle XZM cong. tri. YZM        SSS
      angle XZM cong. to angle YZM     CPCTC
      ZM bisects angle XZY                     def. of bisect


Proof on back page

         statements                                     reasons
angle XZY cong. angle WZV               given
Z is midpoint of YV                              given
YZ is congruent to VZ                          def. of midpoint
angle Y and angle V are rt. angles        given
angle Y congruent to angle V               all right angles congruent
triangle XYZ congruent to tri. WVZ    ASA

Honors Geometry; 11/8

We continued our work with congruent triangles today by taking a look at how to work with 2 pairs of triangles.  The method that was demonstrated in class was called a "key steps proof" , as we shortened the process of using the givens and reflexive parts of triangles.  We went through 3 or 4 together before the students got started on their assignment.


Assignment:  section 4-6;  page 148-150;  WE 1-9, 11, 12

Geometry; 11/7

We continued our work with congruent triangles today by taking a look at how to use triangles to prove various vocab words like midpoint and parallel lines.  All three examples we did involved getting triangles congruent first and then using CPCTC to determine the definition of the vocab word.
The students then took their 2nd proof practice quiz.


Assignment:  section 4-3;  page 129;  CE 2, 3, 5  (write a complete 2-column proof);  page 126;  WE #18

Honors Geometry; 11/3

We went over a few more isosceles triangle problems today using systems of equations from algebra to solve them.  The assignment is a short one!  Have a great weekend.

Assignment: section 4-4;  page 139;  #27-29

Honors Geometry; 11/7

We continued our work with congruent triangles today by going over a few more proofs that involve overlapping triangles.  We continue to use all 5 methods that we have worked on in order to prove triangles congruent. 


Assignment:  section 4-5;  page 143-145;  WE #1-8;  11-14

Geometry: 11/6

Our work today focused on how to use congruent triangles in proofs.  We used congruent triangles to prove other parts of the triangle congruent today.  We went through 3 examples together before taking the first of 3 practice quizzes that we will use this week to prepare for our Chapter 4 quiz on Thursday.


Assignment:  section 4-3;  page 130;  WE #1-4

Honors Geometry; 11/6

We introduced two new methods to prove triangles congruent today:   AAS and the H-L Theorems.  We went over a couple examples of each before the students got started on their assignment.


Assignment:  section 4-5;  page 142;  CE #1-13;  page 146;  Self Test 2;  #1-3;  page 133;  #6

Geometry; 11/3

We continued our work with triangle proofs today by going over 1 more proof together during our shortened class periods.  The students then started working on their assignment....more drawing recognition for congruent triangles.


Assignment:  Section 4-2;  page 124-126;  WE 1-17

Geometry; 11/2

Honors Geometry; 11/2

We worked through the isosceles triangle theorem today with both proofs and some calculations.  The terms vertex angle, base angles, legs, and the base of the isosceles triangle were all introduced and explained. 


Assignment:  section 4-4;  page 137-139;  WE 1-10, 13-17

Geometry; 11/1

We started our new unit today in working with congruent triangles.  We went over what a congruence statement is and how to pick out corresponding parts of triangles from these statements.  We began the process of analyzing drawings in order to spot congruent triangles, as well as reviewed some graphing skills to determine which triangles are congruent as well.


Assignment: section 4-1;  page 120-121;  WE #1-20

Honors Geometry; 11/1

We reviewed a couple more triangle proofs together before taking the chapter 4 quiz in class. 


Assignment:  none;  extra credit puzzle option

Geometry; 10/31

Happy Halloween!   After the students turned in their chapter 3 reviews and entry tasks, they spent the rest of the period working on the chapter 3 test.


Assignment:  none;  extra credit option

Honors Geometry; 10/31

Happy Halloween!  We continued our work with triangle proofs today by going over our practice quiz from yesterday and then modeling another proof together.  The students then took their 2nd practice quiz in class before getting started on the assignment......more practice with proofs and diagrams of congruent triangles.    Chapter 4 quiz is tomorrow.


Assignment:  CPCTC review sheet

CPCTC answers

Example #1

         Statements                                                 Reasons
1.  segment FG cong. to seg. GH                        Given
2.  angle HGJ cong. to angle FJG                        Given
3.  seg. JG cong. to seg. JG                                 reflexive
4.  triangle FGJ cong. to tri. HJG                        SAS post.
5.  seg.  FG cong. to seg. JH                                CPCTC

Example #2

         Statements                                                 Reasons
1.  MP and ON bisect each other                       Given
2.  seg. OX cong. to seg. NX                             def. of bisect
3.  seg. MX cong. to seg. PX                              def. of bisect
4.  angle 1 cong. to angle 2                                vert. angles cong.
5.  triangle MNX cong. tri. POX                       SAS post
5.  angle N cong. to angle O                                CPCTC

Classwork problems

#1
         Statements                                                 Reasons
1.  segment RV cong. to seg. VT                        Given
2.  angle R cong. to angle V                               Given
3.  angle 1 cong. to angle 2                                 vertical angles congruent
4.  triangle STR cong. to tri. WTV                        ASA post.
5.  seg.  ST cong. to seg. WT                                CPCTC

#2
         Statements                                                 Reasons
1.  segment BC cong. to seg. AD                        Given
2.  segment AC cong. to seg BD                       Given
3.  seg. DC cong. to seg. DC                              reflexive
4.  triangle DBC cong. to tri. CAD                    SSS post.
5.  angle BCD cong. to angle ADC                   CPCTC

#3

         Statements                                                 Reasons
1.  R is midpoint of PQ and ST                          Given
2.  segment ST cong. to seg. TR                       def. of midpoint
3.  seg. PR cong. to seg. QR                              def. of midpoint
3.  angle 1 cong. to angle 2                               vert. angles congruent
4.  triangle SRP cong. to tri. TRQ                       SAS post.
5.  angle P cong. to angle Q                               CPCTC

#4

         Statements                                                 Reasons
1.  SQ is perp. bisector of PR                             Given
2.  angle 1 and angle 2 are rt. angles                   def. of perpendicular
3.  angle 1 congruent to angle 2                          all right angles congruent
4.  seg. PQ cong. to seg. RQ                               def. of bisector
5.  seg. SQ cong. to seg. SQ                                reflexive
6.  triangle PQS cong. to tri. RQS                        SAS post.
5.  seg.  PS cong. to seg. RS                                CPCTC

#6

         Statements                                                 Reasons
1.  BD perp. to AB                                              Given
2.  BD perp. to DE                                               given
3.  angle B and  angle D are rt. angles                 def. of perpendicular
4.  angle B cong. to angle D                                 all right angles cong.
5.  seg. BC cong. to CD                                       given
6.  angle 1 cong. to angle 2                                  vertical angles
7.  triangle ABC cong. to tri. EDC                       ASA post.
8.  seg.  AC cong. to seg. EC                                CPCTC

Congruent Triangles Drawings

1.  triangle BIG congruent to triangle FAJ;  SAS
2.  none
3.  none
4.  triangle FLP congruent to triangle VOR;  SSS
5.  triangle HOT congruent to triangle DYA;  SAS
6.  triangle CLD congruent to triangle GNH;  ASA
7.  triangle CAT congruent to triangle MSE;  ASA
8.  none
9.  none
10.  none
11.  triangle QUD congruent to triangle ADU;  ASA
12.  triangle PAT congruent to triangle TYP;  SAS

Geometry; 10/30

We spent some time today going over our chapter 3 review sheet in class.  The students then went through a chapter 3 review scavenger hunt to work on the various topics of chapter 3 one last time.  Once the students were done, they worked on an angle properties review sheet.


Assignment:  Angle Properties Review

Chapter 3 Test tomorrow

Angle Properties Review:

1.  80
2.  60
3.  120
4.  140
5.  120
6.  120
7.  140
8.  80
9.  70
10.  40
11.  70
12.  70
13.  80
14.  80
15.  40
16.  120
17.  60
18.  100
19.  100
20.  140

Honors Geometry; 10/30

We continued to practice our triangle proofs skills together today in class.  We went over the homework and a couple more proofs together.  The students then took a practice proof quiz on their own and worked on the quiz review packet.  We'll get the practice quiz back tomorrow to go over and take another one to get ready for the chapter 4 quiz on Wednesday.


Assignment:  Chapter 4 quiz review

Geometry; 10/27

We spent today reviewing a few proofs involving parallel lines.  The rest of the time was spent getting started on the chapter 3 review packet.  The chapter 3 test is on Tuesday, Oct. 31, and we will go over the review together on Monday.

Assignment:  Chapter 3 review packet

Honors Geometry; 10/27

We continued our work with triangle proofs today by taking a look at how congruent triangles can be used to prove other things.  The concept of CPCTC was introduced and we went through a few more proofs together in order to see how triangle proofs are used to gain extra information about a drawing.  The students then got started on their assignment.

Assignment:  section 4-3;  page 130-131;  WE #1-9 all

Honors Geometry; 10/26

The topic today focused on how to prove 2 different triangles congruent.  We began working with different types of drawings that show to triangles, and illustrated how these drawings can be used to match up corresponding parts of triangles.  We went over 3 triangle postulates today ---  SSS, SAS, and ASA postulates for congruent triangles.  We will continue to work with these in various drawings and proofs over the rest of the chapter.


Assignment:  section 4-2;  page 124-126;  WE  #1-20 all

Geometry; 10/26

Our topic today was going over the concept of inductive reasoning.  We went over how to tell the difference between inductive and deductive reasoning, and how to use the patterns of inductive reasoning to predict the next terms in various number sequences.  We worked through a few word problems together as well before the students got started on their assignment.


Assignment:  section 3-6;  page 107-108;  CE 1-5;  WE 1-17
                            Self Test 2;  page 110;  #1-11

Geometry; 10/25

The topic today involved working with the angles in polygons.  We went over both interior and exterior angles and how to calculate them.  The big key was to determine if the value was a sum of angles or an individual angle.  We went over shortcuts for calculating both of these with 3-4 examples before getting started on the assignment.


Assignment:  section 3-5;  page 104-105;  WE  1-16, 21   (skip #7)

Honors Geometry; 10/25

The students got back their chapter 3 tests today and had a chance to go over them, asking any questions they may have had.  We then got started with the next chapter;  working with congruent figures.  We introduced the concept of a congruence statement and how to determine corresponding parts of congruent triangles.  We also did some simple graphing to determine how congruent figures match up on the grid and how to write the congruence statements.


Assignment:  section 4-1;  page 120-121;  WE 1-21 all;  page 121;  Mixed Review #1

Geometry; 10/24

We continued our work with triangles today by taking a look at the triangle sum theorem and the exterior angles theorem.  Both of these can be used to solve a wide variety of triangle calculations that involve different drawings.  We went through 3 or 4 problem types together before getting started on the assignment.


Assignment:  section 3-4;  page 96;  CE 9-11;  page 97-99;  WE 1-17, 19, 26, 30

Honors Geometry; 10/24

We turned in our ch. 3 reviews and entry tasks to begin the period.  The students then took the rest of the period to take the chapter 3 test.


Assignment:  none;  extra credit puzzle option

Geometry; 10/23

We wrapped up our inductive reasoning project today by taking a look at the overall rules that the graph and tables resulted in.  The next topic in our study of polygons was introduced after this as we went over the different ways to classify triangles either by sides or by angles.  We also began the process of calculating with several different types of triangle drawings.


Assignment:  Classifying Triangles worksheet

Honors Geometry; 10/23

We went over the chapter 3 review worksheet together before working through a drawing activity to review several vocabulary words.  We also went through one more parallel line proof together.  The students then got started on their 2nd chapter 3 review assignment.

Chapter 3 Test is tomorrow.


Assignment:  Chapter 3 Review #2

Practice 9

1.  AIA
2.  Corresponding
3.  SSI
4.  Corresponding
5.  angles 3, 6, and 7
6.  angles 5, 8, 4, and 1
7.  35
8.  55
9.  sometimes
10.  sometimes
11.  never
12.  sometimes
13.  always
14.  always
15.  BE and CF
16.  CE and DF
17.  AD and EF
18.  BE and CF
19.  none
20.  BE and CF;  AD and EF

Practice 10

1.  drawing
2.  drawing
3.  not possible
4.  drawing
5.  40, 50, 90
6.  40
7.  360
8.  9
9.  x = 110, y = 140
10.  a = 55,  b = 80
11.  m = 60,  n = 90
12.  1st row:    6       8       12       8       24
       2nd row:  60     45      30      20      15
       3rd row:  120   135   150     160    165

Practice 11

1.  sometimes
2.  always
3.  sometimes
4.  sometimes
5.  360
6.  90
7.  (n-2) 180
8.  90
9.  x = 17
10.  x = 60;  y = 70
11.  x = 120;  y = 60
12.  -4, 2, -1
13.  4, 16, 8
14.  angle A and angle B are acute
15.  none

Practice 12

1.  angle 8
2.  angle 6
3.  angle 5
4.  x = 9;  angle 1 = 134;  angle 5 = 134
5.  x = 15;  angle 3 = 137;  angle 6 = 43
6.  angle 8 = 45;  angle 6 = 45;  angle 5 = 135
7.  always
8.  sometimes
9.  always
10.  always
11.  sometimes
12.  inductive
13.  deductive
14.  24
15.  angle A = 75;  angle B = 56;  angle C = 49
16.  36

Geometry; 10/20

We continued to work on the inductive reasoning project that we started yesterday.  The students work today was focused on graphing their data and using information about the slope and equation of a line in order to find a pattern in the data they collected.  We demonstrated how to do this on some sample numbers before the students got to work on their own data.


Assignment:  Inductive Reasoning Project    (due Monday)

Honors Geometry; 10/20

This was the first of a couple review days for chapter 3.  We walked through a couple of parallel line proofs together after going over the homework.  The students then had the bulk of the time to work on their chapter 3 review materials.  The chapter 3 test is next week, Tuesday, Oct. 24.

Assignment:  Chapter 3 review sheet

Geometry; 10/19

We got started on the 2nd half of the chapter today by starting work on an inductive reasoning project that deals with polygons.  We will be working on this over the next couple of days.  Today was focused on determining some patterns among the numbers involving the number of sides a polygon has and the sum of its interior and exterior angles.



Assignment:  Inductive Reasoning Project;  page 1 only

Honors Geometry; 10/19

We wrapped up chapter 3 today by taking a more specific look at inductive reasoning.  We went through several examples of number patterns and various described scenarios in which the students needed to decide which kind of reasoning - deductive or inductive - was being used to make decisions.  The students then got started on their assignment.


Assignment:  section 3-6;  page 107-108;  CE 1-5;  WE 1-17;   p. 110;  #1-15 all

Geometry; 10/18

The students turned in their chapter 3 quiz review sheets to start the period.  The rest of the period was spent taking the chapter 3 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 10/18

We continued our work with polygons today by taking a look at other types of polygons  (not triangles).  We used our knowledge gained from the inductive reasoning project to work with both interior and exterior angles of polygons.  We went through a few practice examples together before getting started on the assignment.


Assignment:  section 3-5;  page 104-105;  WE 1-17, 21, 22   (skip #7)

Geometry; 10/17

We spent time today reviewing for our chapter 3 quiz tomorrow.  With partners, the students worked through 8-10 review problems together that are indicative of what they will see tomorrow on the quiz.  They also worked on a review sheet towards the end of the period that will help prepare them for the quiz.  The answers to the review sheet appear below.


Assignment:  Chapter 3 quiz review sheet


Properties of Parallel Lines

1.  skip
2.  skip
3.  AIA
4.  corresponding angles
5.  SSI angles
6.  none
7.  angles 1, 13, and 15
8.  angles 2, 4, and 6
9.  angles 1, 3, 5, 7, 11, 13, 15
10.  angles 2, 4, 6, 8, 10, 12, 14, 16
11.  angle 11 = 55;  angle 15 = 55
12.  angle 4 = y;  angle 3 = 180 - y
13.  x = 70;  y = 90
14.  x = 15;  y = 40

Proving Lines Parallel

1.  GA parallel to EC
2.  GE parallel to AD
3.  GB parallel to ED
4.  none
5.  GB parallel to ED
6.  GB parallel to ED
7.  AD parallel to GE
8.  GB parallel to ED
9.  GE parallel to AD
10.  x = 9;  y = 22
11.  x = 21;  y = 17
12.   proof steps
        1.                                                1.  given
        2.                                                 2.  def. of angle bisector
        3.  angle 1 congruent angle 2      3.
        4.                                                 4.  transitive / subst.
        5.                                                 5.  if AIA congruent, then lines parallel



Solving for x:

19.  x = 4
20.  x = 7
21.  x = 8
22.  x = -7
23.  x = 9
24.  x = 5
25.  x = -6;  angle is 90
26.  x = 4;  angle is 85
27.  x = 10;  angle is 60
28.  x = -9;  angle is 80


Proof #4

statements                                    reasons
l parallel to m                               given
angle 1 cong. angle 2                    given
angle 1 cong. angle 4                   if lines parallel, Corr. angles congruent
angle 2 cong. angle 4                   substitution.


Proof #5

statements                                     reasons
angle 1 cong. angle 2                    given
angle 2 cong. angle 4                    given
angle 1 cong. angle 4                    subst.
line l parallel to line m                 if corr. angles congruent, then lines parallel

Honors Geometry; 10/17

We spent a little time wrapping up the inductive reasoning project before going on to our lesson for today.  Today's topic centered on how to work with triangles with both words and calculations.  We went over several vocab words pertaining to the ways in which triangles are classified.  We then used the triangle sum theorem (all angles sum to 180) to determine a variety of calculation and drawing problems.  The students then got started on their homework.


Assignment:  section 3-4;  page 97-99;  WE 1-20, 26, 28, 30

Geometry; 10/16

We continued our work with parallel lines today by taking a look at how to prove lines parallel.  We use our three angle pairs to work through a variety of drawings in order to determine if lines were parallel or not.  The students then got started on their assignment.

Assignment:    Section 3-3;  page 86;  CE 1-11;  page 87;  WE 1-19

Honors Geometry; 10/16

We continued working on our inductive reasoning project in class today.  The goal today was to graph the information and come up with some general rules from the slope and equation of the lines. 

Assignment:  Finish inductive reasoning project;  due tomorrow

Geometry; 10/12

We continued to work on calculations involving parallel lines and pairs of angles.  We worked through how to handle more complex drawings today and also reviewed how to solve systems of equations.  We did three types of drawings together before getting started on the assignment.


Assignment:  section 3-2;  page 69;  algebra review #10-16;  pg. 81-82;  WE 11-20 all

Honors Geometry; 10/12

The students got back their quiz today and we went over a few of the questions together as a class.  We then began the inductive reasoning project in class that involves working with patterns of angles in polygons.  We will continue this project on Monday.


Assignment:  none

Geometry; 10/11

The lesson today focused on the properties of parallel lines.  These properties have to do with the angle pairs that parallel lines create.  We went over how the AIA are congruent, the corresponding angles are congruent, and the SSI angles are supplemental when lines are parallel.  We worked through a few calculation problems together involving drawings of parallel lines before getting started on the assignment.

Assignment:  parallel lines worksheet +  page 80-81;  WE 1-10

Honors Geometry; 10/11

We turned in the chapter 3 quiz reviews today and then took the chapter 3 quiz in class.


Assignment:  none;  extra credit puzzle

Geometry; 10/10

We started our next unit today by introducing several new vocab words that pertain to parallel lines.  We went over the terms skew and intersections, as well as introduced drawings of corresponding angles, alternate interior angles, and same side interior angles.  All of these angle pairs will be used throughout this chapter in working with parallel lines.


Assignment:  section 3-1;  page 75, CE #10-14 all;  page 76;  WE #1-17 all

Honors Geometry; 10/10

We spent time today in class going over any questions the students had on their parallel lines proofs worksheet.  We then worked through a partner activity involving 10 different review problems that seat partners worked on together.  The students got started on their chapt. 3 quiz review sheet at the end of the period.  Chapter 3 Quiz tomorrow.


Assignment:  Ch. 3 Quiz review



Properties of Parallel Lines

1.  skip
2.  skip
3.  AIA
4.  corresponding angles
5.  SSI angles
6.  none
7.  angles 1, 13, and 15
8.  angles 2, 4, and 6
9.  angles 1, 3, 5, 7, 11, 13, 15
10.  angles 2, 4, 6, 8, 10, 12, 14, 16
11.  angle 11 = 55;  angle 15 = 55
12.  angle 4 = y;  angle 3 = 180 - y
13.  x = 70;  y = 90
14.  x = 15;  y = 40

Proving Lines Parallel

1.  GA parallel to EC
2.  GE parallel to AD
3.  GB parallel to ED
4.  none
5.  GB parallel to ED
6.  GB parallel to ED
7.  AD parallel to GE
8.  GB parallel to ED
9.  GE parallel to AD
10.  x = 9;  y = 22
11.  x = 21;  y = 17
12.   proof steps
        1.                                                1.  given
        2.                                                 2.  def. of angle bisector
        3.  angle 1 congruent angle 2      3.
        4.                                                 4.  transitive / subst.
        5.                                                 5.  if AIA congruent, then lines parallel

When Lines are Parallel

1.  AIA
2.  corr. angles
3.  SSI angles
4.  corr. angles
5.  angles 3, 6, 7
6.  angles 5, 8, 4, 1
7.  35
8.  55
9.  sometimes
10.  sometimes
11.  never
12.  sometimes
13.  always
14.  always
15.  BE parallel to CF
16.  CE parallel to DF
17.  AD parallel to EF
18.  BE parallel to CF
19.  none
20.  BE parallel to CF;  AD parallel to EF

Geometry; 10/9

We answered a few questions at the beginning of the period before the students turned in their chapter 2 entry tasks and reviews.  The rest of the period today was spent taking the chapter 2 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 10/9

We continued our work with parallel line proofs today by going over a couple more together in class.  The students then got started on their assignment, which is a collection of 10 proofs that use different properties of parallel lines and the angle pairs they create.

Assignment:  Parallel Line Proofs worksheet

Geometry; 10/6

We spent some time reviewing the main topics of chapter 2 today with a few proofs and a collection of drawings.  The students then spent the rest of the time working on the chapter 2 review sheet.  The answers will be posted during the weekend so that it can be checked and used to study for the test.  Chapter 2 test is Monday.

Assignment:  Chapter 2 Review sheet


Answers to review sheet

Honors Geometry; 10/6

We continued working with parallel lines and special pairs of angles today.  The topic today was how to use angles to prove that lines are parallel.  We went over 3 different examples together and then showed how to evaluate drawings to find the correct set of parallel lines.  The students then got started on their homework.

Assignment:  section 3-3;  page 87-88;  WE 1-19, 23, 24, 29

Geometry; 10/5

We continued to work with how to do geometric proofs today by going over a couple of samples together.  The students then went through a "pass the proof" activity that allowed them to get some more exposure to in working with proofs.  After seeing 8 different proofs together, the students then got started on their assignment. 

Assignment:  Proof Practice WS #1-20 + proofs #12, 14, 17

Honors Geometry; 10/5

We continued working with parallel lines today by going over the different properties that parallel lines present.  We discussed how corresponding angles are always congruent, AIA are always congruent, and SSI angles are always supplementary when lines are parallel.  We then worked through a few calculation problems together in how to set those kinds of scenarios up from various drawings.  The students then got started on their homework.


Assignment:  section 3-2;  page 80-82;  WE #1-21 all

Geometry; 10/4

We continued our work with proofs today by going over a few more examples of how to put together both columns in a two column proof.  We walked through 2 more together before getting started on the homework and working on some additional practice proofs.


Assignment:  page 62;  CE 10;  section 2-6;  page 63-64;  WE 1-15 all, 20

Honors Geometry; 10/4

The students got back their chapter 2 test today and had the chance to go over it and ask about any questions that they still found confusing.  We then introduced the next lesson as we got started working with parallel lines.  New vocab words were introduced and new angle pairs were also shown that we will be working with quite a bit in terms of parallel lines.  The students then worked on a drawing activity in pairs that they practice their old and new vocab.


Assignment:  section 3-1;  page 76-77;  WE 1-17;  22-29

Geometry; 10/3

We went through how to use perpendicular lines today in various proofs and calculations.  There are three perpendicular line theorems that we went through and modeled how to use these in various proofs.  The students also continued to practice working with supplementary, complementary, and vertical angle calculations.


Assignment:  section 2-5;  page 57;  CE 2-11 all;  page 58-59;  WE 1-16 all

Honors Geometry; 10/3

The students turned in their chapter 2 reviews today before taking the chapter 2 test.  The test took the entirety of the period.

Assignment:  none;  extra credit puzzle option

Geometry; 10/2

We continued our work with types of angles today by going over the next level of calculation problems together.  We took word problems and wrote equations from them using our knowledge of supplementary and complementary angles.  We also used two different variables in problems to choose the correct equation and then solved for both variables.  We ended up by going over one more proof together before getting started on our assignment.


Assignment:  section 2-4;  page 53;  WE 24-28;  +  Angle Pairs Practice worksheet

Honors Geometry; 10/2

We went over our first review sheet and answered any questions that the students had on their homework proofs.  We then worked through a "pass the proof" activity in which students had limited time access to 5 different proofs as we practice and worked on them together.  The students then got started on their 2nd review sheet in preparation for the chapter 2 test tomorrow.


Assignment:  Chapter 2 review #2


Test 7 Answers

1.  congruent
2.  acute
3.  right
4.  obtuse
5.  105
6.  90 - 3y
7.  angle DEB;  angle DGE
8.  angle 3,  angle 2
9.  angle EGD,  angle DGB
10.  angle 1
11.  a.  40       b.  50
12.  angle 7 is congruent to angle 9
13.  complementary
14.  proof steps.
        1.  given
        2.  def. of perpendicular lines
        3.  if ext. sides of 2 adjacent acute angles are perpendicular,
             then the two angles are complementary
        4.  given
        5.   if ext. sides of 2 adjacent acute angles are perpendicular,
             then the two angles are complementary
        6.  given
        7.  complements of congruent angles are congruent themselves

Test 8 Answers

1.  a.  angle 1 and angle 2 are right angles
     b.  angle 1 is congruent to angle 2
     c.  If angle 1 is congruent to angle 2, then angle 1 and angle 2 are right angles.
     d.  false
2.   proof reasons
      1.  given equation
      2.  distributive property
      3.  addition prop. of =
      4.  subtraction prop. of =
      5.  division prop. of =
3.  a.  angle FGE and angle HGI
     b.  angle EGJ and angle IGJ
     c.  angle EGF and angle FGJ
4.  midpoint theorem
5.  def. of perpendicular lines
6.  reflexive
7.  angle bisector theorem
8.  def. of complementary angles
9.  adjacent angles
10.  55
11.  58
12.  52
13.  70
14.  32
15.  a.  13     b.  75
16.  If two lines are perpendicular, then they meet to form right angles.
       If two lines meet to form right angles, then they are perpendicular.
17.   proof statements
          1.                                                   1.  given
          2. m angle 1 + m angle 2 = 90      2.
          3.                                                   3.  angle addition post.
          4.                                                   4.  subst. / transitive
          5.  AB perpendicular to BC          5.
          6.                                                   6.  def. of perpendicular
          7.                                                   7.  substitution / transitive

18.  proof statements
          1. angle 3 and 4 are supp.             1.  given
          2. m angle 3 + m angle 4 = 180    2.  def. of supplemental
          3. m angle 1 + m angle 4 = 180    3.  angle addition post.
          4. angle 3 + angle 4 = angle 1 + angle 4      4.  subst. / transitive
          5. angle 4 = angle 4                      5.  reflexive
          6. angle 3 = angle 1                      6.  subtraction prop. =
          7. angle 3 = angle 2                      7.  vertical angles =
          8.  angle 1 = angle 2                     8.  substitution / trans.
          9.  angle 1 congruent to angle 2   9.  def. of congruent

Geometry; 9/29

We spent today introducing the next topic in our study of proof in geometry.  We went over how to use special angle pairs.  Complementary angles, supplementary angles, and vertical angles were the angle pairs that we worked with today.  Calculations and proof examples were both shown before getting started on the assignment.


Assignment:  section 2-4;  page 52-54;  CE 10-19;  WE 1-21 all

Honors Geometry; 9/29

We spent time today going over homework and reviewing various parts of proofs together.   After a couple of sample proofs, the students then got started on their homework, which was a review sheet and 4 geometric proofs.

Assignment:  Chapter 2 review sheet #1 + proofs 7, 12, 17, and 18

Geometry; 9/28

We took the first few minutes of class to answer any remaining questions on the chapter 2 quiz review sheet.  The students then turned in the reviews and took the rest of the period to complete the chapter 2 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 9/28

We continued our work with how to write geometric proofs.  We now have several more tools to use in this process, so the topic today was planning a proof and how to put them together based on the information we have.  We went through 3-4 more proofs together before getting started on the assignment......more practice proofs!

Assignment:  section 2-6;  page 63-64;  WE 1-17;  19, 20

Geometry; 9/27

We spent time today in class reviewing the different types of questions that will appear on tomorrows quiz.  From algebra proofs to geometric proofs to conditional and biconditional statements, the students had chances to practice each skill in class before getting started on the review sheet.  Chapter 2 quiz is tomorrow.

Assignment:  Chapter 2 Quiz review sheet


Review Sheet answers

Using Deductive Reasoning

1.  hypothesis:  line AB intersects line CD at X
     conclusion:  A, X, and C are coplanar
2.  Hypothesis:  I finish my homework
     conclusion:  I can ride my bicycle
3.  initial statement:  false
     Converse:  If M is midpoint of segment AB, then AM = MB;  converse is true
4.  transitive prop. =
5.  reflexive prop. =
6.  substitution prop. =
7.  symmetric prop. =
8.  addition prop. =
9.  angle bisector theorem
10.  segment addition postulate
11.  angle addition postulate
12.  midpoint theorem
13.  definition of angle bisector

Algebra proof #5                                                        

-3(x + 2) = 16 - x            given                                  
-3x - 6 = 16 - x               distributive prop                
-6 = 16 + 2x                    addition prop. =                
-22 = 2x                          subtraction prop. =            
-11 = x                            division prop. =                

 Algebra proof  #7

6(x - 6) = x(16 - 7)     given
6x - 36 = 16x - 7x      distributive prop.
6x - 36 = 9x                combine like terms
-36 = 3x                       subtraction prop. =
-12 = x                         division prop. =

Properties of Algebra

1.  addition prop. =
2.  division prop. =
3.  multiplication prop. =
4.  subtraction prop. =
5.  division prop. =
6.  distributive prop.
7.  transitive prop. =
8.  symmetric prop. =
9.  addition prop. =
10.  transitive prop. =
11.  subtraction prop. =
12.  skip
13.  skip
14.   proof
           1.  given
           2.  reflexive
           3.  addition prop. =
           4.  segment addition postulate
           5.  transitive / substitution

Proving Theorems

1.  def. of midpoint
2.  def. of angle bisector
3.  midpoint theorem
4.  angle bisector theorem
5.  midpoint theorem
6.  segment addition postulate
7.  angle addition postulate
8.  angle addition postulate
9.  def. of segment bisector
10.  55
11.  65
12.  80
13.  9
14.  8
15.  4.5
16.  3.5
17.  items in a proof
        1.  given                2.  word definitions    
        3.  postulates         4.  theorems

Honors Geometry; 9/27

We continued our work with proofs today by adding the topic of perpendicular lines to the mix.  We went over how to incorporate the definition of perpendicular lines into both calculation problems and proofs.  There were 3-4 examples we went over together before the students got started on their homework assignment.


Assignment:  section 2-5;  page 58-60;  WE  1-25 all, 28

Geometry; 9/26

We continued to work on geometric proofs today by taking a look at how to incorporate the midpoint theorem and the angle bisector theorem into our work.  Both of these theorems were demonstrated together before the students got started on their assignment.


Assignment:  section 2-3;  page 45;  CE 1-10;  page 46;  WE 1-14

Honors Geometry; 9/26

The students got back their chapter 2 quiz today and were able to ask any questions that they may have had.  We also moved on in our study of proofs to take a look at special pairs of angles.  We went over complementary, supplementary, and vertical angles today.  We demonstrated how to do both calculation problems and proofs using these pairs of angles.

Assignment:  section 2-4;  page 52-54;  WE  1-33 all