Geometry; 11/30

We started class today by explaining a scavenger hunt project that we will be working on over the next two and a half weeks.  The project is explained in a packet that I handed out with various examples and scoring standards.  The due date is Wednesday, Dec. 16.

Our lesson today focused on a few more theorems involving parallel lines that can be used when working with parallelograms.  We went over these three theorems and several examples that show how they are used in calculations.  The students then got started on their homework.

Assignment:  section 5-3;  page 180-181;  WE  #1-16 all;  page 182;  Self Test 1    #1-6 all


Our next quiz will take place this Wednesday over sections 5.1 to 5.3

Honors Geometry; 11/30

We reviewed the concept of properties of inequalities today with a short proof before going through a few examples of some new ways to deal with conditional statements.  Today's lesson focused on using the vocab words converse and contrapositive in a variety of different statements.  We also showed how Venn diagrams can be used to solve these new types of logic problems.


Assignment:  section 6-2;  page 210-212;  WE  #1-18 all

Geometry; 11/25

We went over our calculations with parallelograms worksheet today to begin the class.  We then spent the rest of the shortened period working on a geometric building activity using toothpicks.


Assignment:  none;    Happy Thanksgiving

Honors Geometry; 11/25

We went over our homework from section 6-1 today to begin the class.  We then spent the rest of the shortened period working on a geometric building activity using toothpicks.


Assignment:  none;    Happy Thanksgiving

Geometry; 11/24

We continued our work with parallelogram proofs today by going over two more examples together and then working through a calculation problem involving all 5 properties of parallelograms that we have studied.  The students then got started on their assignment.


Assignment:  Parallelogram Calculations worksheet

Honors Geometry; 11/24

We returned the chapter 5 test today and began our study of chapter 6.  The topic today involved an introduction to inequalities in triangles.  We went through some examples of how inequalities are used in algebra, and how they can be applied to geometric drawings as well.  The use of these properties of inequalities was demonstrated through 3-4 diagrams before the students got their assignment.

Assignment:  section 6-1;  page 205;  CE  #1-16;  page 206;  WE  #1-8

Geometry; 11/23

We continued our work with parallelograms today by taking a look at how to prove parallelograms from various drawings.  We worked a couple more parallelogram proofs together and also added another property of parallelograms to our growing chart.  The additional property is that a parallelogram can also be found if one pair of opposite sides are both congruent and parallel.


Assignment:  Proving Parallelograms worksheet

Honors Geometry; 11/23

We turned in our chapter 5 review sheet today and then took the chapter 5 test in class.  An extra credit puzzle was also available after the test.


Assignment:  none

Geometry; 11/20

We started a new chapter today by talking about the properties of parallelograms.  We went over 4 different properties and how they are used in calculations before getting started with the homework assignment.


Assignment:  section 5-1;  p. 168;  CE  #3-8 all;  p. 169-170;  WE  #1-12 all,  17-21 all

Honors Geometry; 11/20

We went over the homework together and then completed our quadrilaterals chart by talking about the unique properties of kites today.  We then went over one more parallelogram proof together before getting started on the review sheet.  Chapter 5 Test will be on Monday, Nov. 23


Assignment:  Chapter 5 Review Sheet


Chapter 5 Review Sheet Answers

Practice 20

1.  true
2.  false
3.  false
4.  true
5.  false
6.  Q
7.  RQ
8.  7.5
9.  3.7
10.  trapezoid
11.  6
12.  x = 3 and DF = 18
13.  angle GFE = 92 and angle DEF = 88
14.  rectangle
15.  angle WXY is congruent to angle WZY
16.  WX is parallel to ZY or WZ is congruent to XY
17.  WX is parallel to ZY or WZ is congruent to XY
18.  ZP is congruent to PX
19.  Drawing the quadilateral and drawing in an auxiliary line between ZX to form two triangles is necessary to fully understand the proof.

                 Statements                                                               Reasons
angle XWZ congruent to angle XYZ                               given
WX parallel to ZY                                                            given
angle WXZ congruent to angle XZY                               if lines parallel, AIA congruent
ZX congruent to ZX                                                         reflexive
triangle XWZ congruent to triangle ZYX                        AAS
WX congruent ZY                                                            CPCTC
WXYZ is parallelogram                                                   If one pair of opp. sides are both
                                                                                        congruent and parallel, then quad,
                                                                                        is parallelogram

Quadrilaterals Sheet

1.  angle ABC = 92;  angle DAB = 88
2.  BE = 10
3.  x = 2
4.  x = 3
5.  AE = 13.4
6.  angle AED = 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 also midpoint of HG
11.  angle A;  DE = 13
12.  BE = 24
13.  trapezoid
14.  median
15.  isosceles trapezoid
16.  PA = 18
17.  angle A = 80;  angle TMN = 80
18.  rectangle
19.  rhombus
20.  isosceles trapezoid

Test 20 sheet

1.  triangle YWX
2.  angle XYZ
3.  110
4.  a.  30      b.  64
5.  a.  12       b.  6
6.  4
7.  rectangle
8.  rhombus
9.  parallelogram
10.  rectangle
11.  rhombus
12.  square
13.  sometimes
14.  sometimes
15.  never
16.  sometimes
17.  median
18.  a.  115      b.  65
19.  7

Geometry; 11/19

We turned in the chapter 4 review packet at the beginning of the period and then took the period to then take the chapter 4 test.

Assignment:  none;  extra credit puzzle option after the test

Honors Geometry; 11/19

We worked on another special type of quadrilateral today by focusing on trapezoids.  We went over how to work calculation problems with trapezoids and also how to work with isosceles trapezoids.  We went through several examples together before getting started on the homework.


Assignment:  section 5-5;  page 192-194;  WE  #1-27 all, 30, 32

Geometry; 11/18

We spent some time reviewing our diagrams and vocabulary from chapter 4 today with a classroom whiteboard activity.  We also went over a couple of isosceles triangle calculations problems together.  The students spent the rest of the time working on their chapter 4 review sheet in preparation for the test tomorrow.


Assignment:  Chapter 4 review sheet

Chapter 4 Test tomorrow


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


Fill in the Blank Proof worksheet

1.  AB parallel to DC
                                                                               2.  if lines parallel, then AIA congruent
3.  angle B congruent to angle D
                                                                               4.  reflexive
                                                                               5.  AAS
6.  BC congruent to DA



1.  QK congruent to QA
                                                                               2.  given
3.  angle 1 congruent to angle 2
4.  QB congruent to QB
                                                                               5.  SAS
6.  KB congruent to AB                                         6.  CPCTC



1.  BD perp. to AB;  BD perp. to DE                     1.  given
                                                                                2.  def. of perpendicular
3.  angle B congruent to angle D                            3.  all right angles congruent
                                                                                4.  vertical angles congruent
                                                                                5.  given
6.  tri. ABC congruent to tri. EDC                          6.  AAS congruent theorem
7.  angle A congruent to angle E                             7.  CPCTC



1.  FJ congruent to GH                                          1.  given
2.
                                                                               3.  reflexive
4.  tri. JFH congruent to GHF                                4.  SAS congruence postulate
5.  FG congruent to JH                                           5.  CPCTC



                                                                               1.  given
2.  angle P and angle N are right angles        
3.  angle P congruent to angle N
4.  MN congruent to MP
5.  MO congruent to MO                                        5.  reflexive
6.  tri. MPO congruent to tri MNO                         6.  HL congruence theorem
7.  angle NOM congruent to angle POM                7.  CPCTC



1.  CN perp. to AB                                                1.  given
                                                                              2.  def. of perp.
3.  angle ANC congruent to angle BNC               3.  all right angles are congruent
4.  CN bisects angle ACB
5.  angle 1 congruent to angle 2                           5.  def. of bisect
6.  CN congruent to CN                                       6.  reflexive
7.  tri. ANC congruent to tri. BNC                      7.  ASA congruence postulate
8.  AC conguent to BC                                        8.  CPCTC
9.  tri. ABC is isosceles                                       9.  def. of isosceles triangle

Honors Geometry; 11/18

We continued working with special parallelograms today by showing how to take some calculations shortcuts as we worked problems with a rectangle, a rhombus, and a square.  We also went through a parallelogram proof showing how to use these different figures as well.


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

Geometry; 11/17

We went through the final section of chapter 4 today by taking a look at the meanings of 3 vocabulary words and their drawings:  medians, altitudes, and bisectors.  We went over a few different examples of how to draw these figures and some of the information that congruent triangles can provide us when working with them.


Assignment:  section 4-7;  page 155;  CE  #1-9;    +  section 4-6/4-7 worksheet

Honors Geometry; 11/17

We went over the chapter 5 quiz today to start the period.  We then went through a lesson the properties of some special cases of parallelograms.  The rectangle, the rhombus, and the square were all examined to see how their special properties fit into the larger overall picture of parallelograms and quadrilaterals.



Assignment:  section 5-4;  page 186-187;  CE  #1-10 all;  WE  #1-10 all

Geometry; 11/16

The topic for today focused on how to work with two sets of congruent triangles within one proof.  We went through a couple of examples, and then did some streamlined examples of key steps to a proof in which not all the details are included in the writing of the proof.  The students then got started on their assignment.


Assignment:  section 4-6;  page 148-149;  WE  #1-8 all;    page 151;  Mixed Review Ex.  #1-10 all

Honors Geometry; 11/16

After turning in our review sheet, the students spent the period taking the chapter 5 quiz.  After the quiz, the students could work on an extra credit puzzle if they chose to.


Assignment:  extra credit puzzle

Geometry; 11/13

We went over 2 more overlapping triangle proofs together before the students got started on a proof worksheet that deals with all 5 types of triangle congruence methods.


Assignment:  CPCTC worksheet

Honors Geometry; 11/13

We worked through a couple of parallelogram proofs today before getting started on a review assignment dealing with sections 5-1 to 5-3.  This review packet will help the students prepare for the chapter 5 quiz on Monday.  The answers to the review will be posted later on this weekend.


Assignment:  Chapter 5 quiz review packet


Chapter 5 Review Packet answer key

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

8.  x = 25;  y = 11
9.  x = 95;  y = 85

10.  AB = 4;  BC = 6;  CD = 4;  AD = 6
11.  AB = 7;  BC = 5;  CD = 7;  AD = 5

12.  two column proof

Statements                                                        Reasons
angle W and angle X are supp.                        given
angle X and angle Y are supp.                         given
angle Y and angle Z are supp.                          given
m angle W + m angle X = 180                     def. of supplementary
m angle X + m angle Y = 180                      def. of supplementary
m angle X + m angle Y = m angle X + m angle W      substitution
m angle Y = m angle W                                subraction prop. =
angle Y is congruent to angle W                   def. of congruence
m angle Y + m angle Z = 180                        def. of supplementary
m angle X + m angle Y = m angle Y + m angle Z     substitution
m angle X = m angle Z                                  subtraction prop. =
angle X is congruent to angle Z                    def. of congruence
WXYZ is parallelogram                               if both pairs of opp. angles are congruent,
                                                                     then figure is parallelogram

Theorems involving parallel lines practice worksheet

1.  x = 6
2.  x = 7
3.  QS = 40
4.  PR = 12;  PS = 18
5.  RS = 7
6.  x = 10
7.  x = 5
8.   points C and A
9.  Points B and C
10.  points B and A
11.  YZ = 12
12.  MN = 10
13.  x = 25;  MN = 25;  YZ = 50
14.  angle XYZ = 40

Geometry; 11/12

We went over two more methods of how to prove triangles congruent today.  The AAS and the H-L methods were demonstrated today via a couple of proofs and several diagrams.  We also went over the first of several proofs that we will see that deal with overlapping triangles.


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

Honors Geometry; 11/12

We continued our work with chapter 5 today by going over 4 new theorems that involve parallel lines.  These theorems introduced multiple parallel lines and the segments that different transversals cut off.  We also demonstrated what a midsegment of a triangle is and how to work calculation problems using midsegments.


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

Geometry; 11/11

No school;  Veteran's Day Holiday

Honors Geometry; 11/11

No school;  Veteran's Day Holiday

Geometry; 11/10

We went over the answers to the chapter 4 quiz review sheet at the beginning of the period.  The students then spent the period completing the chapter 4 quiz.  After the quiz, the students then got started on their assignment.


Assignment:  page 132-133;  Self Test 1;  #1-8 all

Honors Geometry; 11/10

We continued working with parallelograms today by showing how to use the properties to prove that various quadrilaterals are parallelograms.  We showed 6 different methods to prove that quadrilaterals are parallelograms and began using them in parallelogram proofs.


Assignment:  section 4-2;  page 174-175;  WE  #1-10; 14-17;  19-22

Geometry; 11/9

We went over our last proof quiz today before reviewing for the quiz tomorrow.  We then went over 4-5 examples that seemed to be the most difficult from the practice quizzes last week.  The students then got started on their review sheet.


Assignment:  Section 4.1 to 4.4 review sheet

Quiz tomorrow

Honors Geometry; 11/9

We started chapter 5 today on quadrilaterals by talking about the properties of parallelograms.  There are 5 main properties that we will use throughout this chapter and we showed how they all stem from congruent triangles and sets of parallel lines.  We went through several examples together before the students got started on their assignment.


Assignment;  section 5-1;  page 169-170;  WE   #1-32;  skip every third problem

Geometry; 11/5

We went over both the homework and the proof check quiz to start the period.  Today's topic focused on the isosceles triangle theorem and how to work calculation problems involving isosceles triangles.  We went through 4-5 examples together before the students took another proof check quiz and got started on their assignment.


Assignment:  section 4-4;  page 137;  WE  #1-10

Honors Geometry; 11/5

The students turned in their chapter 4 review sheet today and then took the chapter 4 test.


Assignment:  extra credit puzzle option

Geometry; 11/4

We went over our first proof check quiz as well as the homework together to start the period.  We then took a look at how to incorporate vocabulary words into proofs.  The three proofs we went through today focused on how to prove vocabulary words at the end of the proof from the drawings provided.  The students then took their second proof check quiz before getting started on their assignment.


Assignment:  section 4-3;  page 129;  CE  #1, 2, 3, 5

Honors Geometry; 11/4

We continued our review today by answering questions from the first review sheet to begin the period.  We then went over 2-3 more proofs together from the proof packet before the students got started working on their 2nd review sheet.  The answers to that review sheet appear below.

Assignment:  Chapter 4 review sheet #2

Chapter 4 Test tomorrow



1.  triangle RPD
2.  angle Q;  angle R
3.  segment DE congruent to segment GH
     segment EF congruent to segment HK
     segment DF congruent to segment GK
4.  a.  vertical angles congruent      b.  SAS    c.  CPCTC
5.  a.  yes, ASA       b.  no
6.  3
7.  equiangular; equilateral
8.  median
9.  obtuse
10.  15
11.  if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
12.  a.  angle ADB,  angle CDB
       b.  if a point is equidistant from the sides of an angle, then the point lies on the angle bisector of the angle.
13.  proof
                       Reasons                                         Statements
               RT is perp. to plane P                            given
           angle KTR and angle ZTR rt. angles         def. of perp.
               RK cong. RZ                                          given
               RT cong. RT                                          reflexive
            triangle RKT cong. triangle RZT             HL
              KT cong. ZT                                           CPCTC
           triangle KTZ is isosceles                           def. of isosceles triangle

14.  proof
                       Reasons                                       Statements
          YW is altitude of triangle XYZ                 given
           angle 1 and angle 2 are rt. angles              def. of altitude
           angle 1 cong. angle 2                                 all rt. angles cong.
           angle X cong. angle Z                                given
           YW cong. YW                                           reflexive
           triangle YXW cong. triangle YZW           AAS
           XW cong. ZW                                           CPCTC
           W is midpoint of XZ                                 def. of midpoint
           YW is a median of triangle XYZ              def. of median

15.  proof
                      Reasons                                       Statements
      PO is perpendicular bisect. of QR               Given
     PQ is congruent to PR                                 If pt. lies on perp. bisector of segment,
                                                                         then pt. is equidistant from the endpoints
                                                                         of the segment.
     angle Q congruent angle R                         if opp. sides are congruent, then
                                                                         base angles are congruent
     angle R congruent to angle 1                      vertical angles congruent
     angle Q congruent to angle 1                      transitive property

Geometry; 11/3

We continued working on congruent triangle proofs today with an extra step added on.  We went over how to use corresponding parts of congruent triangles in proofs today, using CPCTC as the abbreviation as the reason in the proof.   We then took the first of 4 proof check quizzes on triangle proofs.


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

Honors Geometry; 11/3

We went through the first of our review days today for the Chapter 4 test.  We answered questions and went through a couple of proofs together before starting work on a review sheet.


Assignment:  Chapter 4 Review Sheet #1


Proof Packet due on Monday, Nov. 9

Chapter 4 Test on Thursday, Nov. 5

Geometry; 11/2

After going over the homework, we continued working with triangle proofs today by showing 4-5 examples of how to do 2-column triangle proofs.  This will be an emphasis this week before our quiz on Thursday.  The students then got started on their assignments.


Assignment:     congruent triangle worksheet   +  page 126  WE  #17-19

Honors Geometry; 11/2

We spent time today going over the last section of chapter 4.  Today's lesson focused on three separate vocab words and how they relate to triangles.  We demonstrated together what a median is, what an altitude is, and how to work with both segment and angle bisectors in triangles.  We went over several examples together before the students got started on their assignment.


Assignment:  section 4-7;  page 155;  CE  #1-7;   page 156-158;  WE  #1-13, 20, 23, 24

Geometry; 10/30

We started our work with congruent triangle proofs today by taking a look at three different ways to prove triangles congruent.  We went over how to use the SSS, ASA, and SAS method of triangle proofs today and also showed the first examples of two column triangle proofs.  We will continue working on these next week as we move through the chapter.


Assignment:  section 4-2;  page 124-125;  WE  #1-16 all

Honors Geometry; 10/30

We continued with our work on triangles today by taking a look at pairs of congruent triangles.  We went over how to work with two pairs of triangles at the same time in order to solve problems.  In each case, one pair was solved first, and then part of the first pair was used in order to figure out the second set of triangles.  The phrase "key steps of a proof" was also introduced today in our work.

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