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