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