Geometry; 11/30

We answered several homework questions today on how to work with midpoints and systems of equations.  We then did our final two practice proofs using parallelograms.  There is one of these on the quiz tomorrow, so everyone got one last chance to hone their proof skills.  The rest of the period was used to work on the ch. 5 quiz review assignment.


Assignment:  Chapter 5 quiz review WS


Ch. 5 Quiz tomorrow

Review Sheet Answers:

Page 1

1.  parallel and congruent
2.  congruent and parallel
3.  congruent
4.  diagonals
5.  yes;  both diagonals bisect
6.  no;  only one set of opp. sides are parallel
7.  no;  only 1 set of opp. sides are parallel
8.  no;  only 1 set of opp. sides are congruent
9.  x = 3;  y = 2
10.  x = 37;  y = 22
11.  x = 9;  y = 10

pg. 173;  CE  #1-9

1.  yes;  both pair of opp. sides congruent
2.  yes;  one pair of opp. sides are congruent and parallel
3.  no;  only one diagonal bisects
4.  yes;  both diagonals bisect
5.  no;  only 1 pair of opp. angles are congruent
6.  yes;  both pair of SSI angles are supplementary
7.  yes;  both pair of opp. sides are parallel
8.  no;  only 1 pair of opp. sides are congruent
9.  yes;  both pair of opp. sides are parallel

Midsegment Problems

1,  x = 8; y = 10; z = 10
2.  x = 6.5
3.  x = 20
4.  x = 9
5.  x = 31
6.  x = 10
7.  x = 60; y = 140
8.  x = 8.75;  y = 15
9.  x = 50
10.  x = 6;  y = 6.5

Theorems Involving Parallel Lines

1.  true
2.  false
3.  true
4.  true
5.  x = 20; y = 10
6.  x =5; y = 3
7.  15
8.  27
9.  6
10.  2a
11.  84
12.  70
13.  72
14.  7
15.  16
16.  6
17.  2

Honors Geometry; 11/30

We went through our final topic of chapter 5 today dealing with trapezoids.  We demonstrated how to identify parts of the trapezoid and then use these parts in various types of calculations.  We went through how to find the midsegment and the lengths of the bases in 3-4 problems together before the students got started on their assignment.


Assignment:  section 5-5;  page 192-194;  WE  #1-25;  page 195;  #1-7

Geometry; 11/29

We continued to work with properties of parallel lines today by going over 3 new theorems together.  We worked on finding the distance between parallel lines, using parallel lines and two sets of transversals, and then went over what a midsegment is and how to use it in various calculations.  We went through 3-4 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; 11/29

We continued our work with special parallelograms today by taking a look at how to work calculation problems using the properties of rectangles, rhombi, and squares.  We went over 4-5 together, as well as doing a proof together using these properties.  The students then got started on their assignment.


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

Geometry; 11/28

We spent the first part of the period taking a practice quiz on the material that we learned last week.  This review session was just a refresher to help us get caught up with what we were working on today.  The lesson that we went over today focused on how we can look at a diagram to prove that it is a parallelogram.  We went through one more sample proof together to come up with a sixth property of parallelograms before then showing several recognition diagrams that the students will be working on in their assignment.  We did 5-6 recognition drawings together before the students got started on their homework.


Assignment:  Proving Parallelograms WS + Practice Quiz  (finish)

Honors Geometry; 11/28

We returned from Thanksgiving Break this morning to do a little review about parallelograms before getting started with the lesson.  This review exercise will be a helpful review tool for the end of the week in getting ready for the test.  The lesson today focused on the special properties of rectangles, rhombi, and squares.  We went over each shape quickly to point out some of its unique properties as parallelograms before getting the students started on their assignment.

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

Chapter 5 Test coming up on Friday, Dec. 2

Geometry; 11/23

We went over our homework assignment together and answered any questions the students had.  We then spent the remainder of our shortened periods working on several different geometric problem solving puzzles using toothpicks!


Assignment:  none

Happy Thanksgiving!

Honors Geometry; 11/23

We returned the chapter 5 quiz today and went over any questions that the students might have had.  We then spent the remainder of our shortened periods working on several different geometric problem solving puzzles using toothpicks!


Assignment:  none

Happy Thanksgiving!

Geometry; 11/22

We continued our work with parallelograms today by taking a look at how to write parallelogram proofs.  We went through a few together, and found that they are really just triangle proofs that use the various properties of parallelograms.  We continued to work on the calculations of the properties of parallelograms as well with some various practice problems on the entry task and homework assignment.

Assignment:  parallelogram worksheet + page 169-170;  WE  16, 30, 32

Honors Geometry; 11/22

We answered a few questions together from our chapter 5 quiz review sheet to start class.  The students then turned in the review sheets and then took the ch. 5 quiz.


Assignment:  extra credit puzzle option

Geometry; 11/21

The students got back their chapter 4 test today and we went over any questions they had.  We then got started on our new unit which involves the study of quadrilaterals.  Today's lesson focused on the properties of parallelograms.  We went over 5 facts that can be used when working with parallelograms.  We went through a few sample calculation problems before the students got started on their assignment.


Assignment:  section 5-1;  page 169-170;  WE  #1-12 all, 17-24 all

Honors Geometry; 11/21

We continued working on parallelogram proofs today by going over a couple more together in class.  The method of finding congruent triangles first was used in each example, and the triangles were found to be congruent by using the various properties of parallelograms.

Our chapter 5 quiz (5.1 to 5.3) is tomorrow in class.


Assignment:  Chapter 5 Quiz review sheet


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   (odd problems only)

1.  true
2.  false
3.  true
4.  true
5.  x = 20, y = 10
6.  x = 5, y = 3
7.  15
8.  27
9.  6
10.  2a
11.  84
12.  70
13.  72
14.  7
15.  16
16.  6
17.  2

Practice 18:  Parallelograms

1.  4
2.  5
3.  120
4.  20
5.  3
6.  7
7.  105
8.  x = 10
9.  x = 6
10.  always
11.  always
12.  sometimes
13.  never
14.  x = 11,  y = 16
15.  x = 26,  y = 15
16.  x = 11, y = 4

Geometry; 11/18

We turned in our chapter 4 review sheets and entry task sheets before taking the chapter 4 test in class.


Assignment:  extra credit logic puzzle option

Honors Geometry; 11/18

We went over the homework last night, emphasizing the 4 proofs involving parallelograms.  We then went through today's lesson that focused on more theorems involving parallel lines.  We talked more about equidistance between parallel lines and how this can be used to solve various types of problems.  We also introduced the concept of a midsegment in a triangle and how the properties of midsegments can be used in working with parallel lines.  The students then got started on their assignment.


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

Geometry; 11/17

We spent some time reviewing vocabulary from chapter 4 today with a couple of overlapping proofs.  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; 11/17

We continued our work with parallelograms today by going over how to prove that shapes are parallelograms.  We used the 5 facts from yesterday as well as adding one additional theorem today that can be used in parallelogram proofs.  We went over a few examples together before getting started on the homework assignment.


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

Geometry; 11/16

We wrapped up chapter 7 today by going over 3 different drawings of features of triangles.  We demonstrated what an altitude, median, and two types of bisectors are when drawn in a triangle.  We went through 3-4 examples of them before getting started on the homework assignment for the day.


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

Honors Geometry; 11/16

The students got back their chapter 4 test today and we went over any questions that they had.  We then started our next unit that will find us studying quadrilaterals.  Today's topic focused on parallelograms and the unique properties they possess because of their opposite sides being parallel.  We went through 3-4 theorems together before showing the students how to use these theorems to do a variety of calculation problems.


Assignment:  section 5-1;  page 169-170;  WE  #1-12, 17-28

Geometry; 11/15

We introduced the concept of how to work with 2 pairs of congruent triangles today.  Finding the key steps in a proof is a way to both shorten a proof and to work with two sets of triangles in the same problem.  We went through 3 of these examples together before the students tried a couple on their own.  They then got started on their assignment.


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

Honors Geometry; 11/15

We turned in our review assignments and entry tasks from chapter 4 today at the start of the period.  The remainder of the period was then spent taking the chapter 4 test.


Assignment:  finish proof packet for ch. 4;  due tomorrow
                      optional extra credit puzzle

Geometry; 11/14

We continued our work with congruent triangles today by taking a look at how to work with drawings that have overlapping triangles.  We now have 5 methods to choose from, so being able to decipher the drawings becomes more and more important.  We went through three examples of overlapping triangles in proofs together before the students got started on their assignment.


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

Honors Geometry; 11/14

We went over our proof quiz from last week together today in preparation for the test tomorrow.  We also went over any questions that the students had on their chapter 4 review sheet.  The students then got to work on an additional review sheet in getting them ready for the test.  The chapter 4 proof packet will be due on Wednesday, Nov. 16.  Students were working on that in class today as well.


Assignment:  Chapter 4 Review #2    

Chapter 4 Test tomorrow


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; 11/10

We continued our work with triangle proofs today by going over the AAS theorem and the H-L theorem  (hypotenuse leg).  These two additional methods of proving triangles were demonstrated and practiced together before the students got started on their homework assignment.


Assignment:  CPCTC worksheet for proving triangles

Honors Geometry; 11/10

We spent some time this morning going over a couple of proofs from the proof packet.  We then took our chapter 4 proof quiz involving overlapping and pairs of triangles.  We will get this back on Monday and go over it to help us prepare for the test on Tuesday.


Assignment:  Chapter 4 Review worksheet


Chapter 4 Test:  Tuesday, Nov. 15

Geometry; 11/9

We continued on in our study of triangles today by going over how to work with isosceles triangles in both proofs and calculations.  We went over the definition and parts of the isosceles triangles before demonstrating both isosceles triangle proofs and some drawing calculations.  Use of the triangle sum theorem (angles add to 180 degrees) is what we will make use of quite often for these problems.  The students then got started on their homework.


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

Honors Geometry; 11/9

Today's lesson focused on using the vocab words of median, bisector, and altitude in various types of proofs.  We went over two additional proofs together before the students kept working on their proof packet.  The suggested proofs for today were the #5-9.   There will be a short proof quiz tomorrow in class.


Assignment:  Proof Packet questions  #5-9

Geometry; 11/8

We turned in our review sheet today before taking the chapter 4 quiz.  The students had the period to work on the quiz.  An extra credit puzzle option was available after the quiz was completed.



Assignment:  extra credit puzzle option

Honors Geometry; 11/8

We continued our work with proofs today by taking a look at how 3 different vocabulary words factor into triangle proofs.  We went over the terms median, altitude, and bisector today.  Each one has a special application in our work with triangles and we will get more into their proof application tomorrow.  Today was just to familiarize the students with the terms and the drawings that go along with them.

Assignment:  section 4-7;  page 155;  CE  #1-7;  page 156-158;  WE  1-13, 20  (skip #6)

Geometry; 11/7

We got back our last proof check quiz today and went over it together.  We then spent some time reviewing some key concepts on the chapter 3 quiz tomorrow.  The bulk of the period was then spent working on the review sheet for the chapter 3 quiz.


Assignment:  Chapter 3 quiz review WS +  page 133;  #8

Honors Geometry; 11/7

We continued on with our study of congruent triangles today by going over how to work with 2 pairs of congruent triangles in drawings.  We illustrated a few of these types of problems and introduced the concept of just showing the key steps in a proof.  Both triangle pairs are necessary in order to solve the problem in each case, and there is a pattern to each problem that the students were able to see.


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

Geometry; 11/4

We went over our proof quiz from yesterday and then took the last proof check quiz today in class.  After the quiz, the students got started on their assignment.


Assignment:  page 132-133;  Self-Test 1;  #1-7

Honors Geometry; 11/4

We went over the homework from last night and answered several questions before turning in the assignment.  We then spent the last 10-15 minutes of the shortened periods getting started on the chapter 4 proof packet.  We will be working on this throughout next week as well.


Assignment:  Proof Packet;  #1-4

Geometry; 11/3

We continued our work with triangle proofs today by taking a look at how to prove symbols and words using a two column proof.  We went over a couple of examples in class before taking our 3rd proof check quiz.  The students then got started on their assignment after the quiz.


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

Honors Geometry; 11/3

We continued our work with congruent triangle proofs today by taking a look at a few more drawing types in which the triangles overlap.  These diagrams include the AAS and HL theorem that we introduced yesterday, but can also involve any of the previous 3 that we have worked on.  After a few examples, the students got started on their assignment.


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

Honors Geometry; 11/2

We continued our work with triangle proofs today by going over two more methods of proving triangles congruent.  The AAS method and the H-L method were the two that we introduced.  The AAS method is closely related to ASA, but it has a non-included side.  The Hypotenuse-Leg theorem only works with right triangles due to the relationship of the sides spelled out by the pythagorean theorem.  We went over a few proofs to illustrate these concepts before the students got started on their assignment.


Assignment:  section 4-5;  page 142;  CE  #1-13 all;  page 133;  #6, 7

Geometry; 11/1

We continued our work with congruent triangle proofs today by taking a look at a couple more proofs together as a group.  We used parallel lines and different vocabulary words in the proofs we worked on today.  The students then took a short practice quiz that we will be using to get used to what proof quizzes look like.  After doing these two proofs, the students then got started on their assignment.

Assignment:  section 4-2;  page 124-126;  WE  1-19 all

Honors Geometry; 11/1

We got the chapter 4 quiz back from yesterday!  Great scores, as the overall average of both classes was 88%!  16 students received scores of 100 or above!  Super job!   Our lesson today focused on continuing to work with triangle proofs and how to use isosceles triangles in those proofs.  We went over a couple new theorems about isosceles triangles and then demonstrated some calculation shortcuts that can be used when working with these types of triangles.  The students then got started on their homework.


Assignment:  section 4-4;  page 137-139;  WE  #1-10, 13-17, 23, 27