Geometry; 10/31

We got back the chapter 3 test today before getting started with the lesson.  Today's lesson focused on ways to prove triangles congruent.  We went over 3 of the methods today in class:  SSS, ASA, and SAS.  These postulates are ones that we will use quite a bit this chapter and will need to be recognized quickly in drawings and proofs.  We went over a few drawing recognition exercises together before the students got started on their homework.


Assignment:  Congruent triangle drawings packet +  1 proof on the screen

Honors Geometry; 10/31

We turned in the review assignment for the chapter 4 quiz to start off the period.  The students then spent the period taking the chapter 4 quiz.


Assignment:  Extra credit puzzle option

Geometry; 10/28

We started chapter 4 today dealing with congruent figures.  We went over some drawing recognition today as we start to build a foundation for what we will be working with later in the chapter.  The focus of the lesson centered on lining up corresponding parts of figures and using the correct order of letters to match them up.  There were also a couple of graphing exercises that were introduced as well.


Assignment:  section 4-1;  page 120;  WE  #1-19 all

Honors Geometry; 10/28

We continued working on triangle proofs today by going over our practice quiz from yesterday and taking another practice quiz today.  The students got answers to their questions on the review sheet, and got a final review assignment to prepare them for Monday's quiz.  The best way to study is to look over the collection of proofs that we have worked on and know the different ways to use the SSS, ASA, and SAS postulates.

Assignment:  CPCTC worksheet packet

Quiz on Chapter 4-1 to 4-3 on Monday, Oct. 31.


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; 10/27

We turned in our review sheets and entry tasks for chapter 3 today and then took the chapter 3 test in class.


Assignment:  extra credit puzzle optional

Honors Geometry; 10/27

We continued to work on how to use congruent triangles to solve various types of proofs.  We went through two more examples today before having the students take a short practice quiz.  They will get this back tomorrow and we will go over their review sheets then.


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

Geometry; 10/26

We spent some time at the beginning of the period answering any questions from the review sheets.  We then went over a couple more proofs before getting started on the angle review puzzle.  We worked on this and a parallel line review in class and compared answers before we left.  The chapter 3 test is tomorrow and we will turn the review sheets in then.


Assignment:  Angle properties review + proofs review


Answers appear below.

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

Parallel Lines Review

1.  lines l and t
2.  lines j and k
3.  lines l and t
4.  lines j and k
5.  lines l and t
6.  none
7.  lines j and k
8.  lines j and k
9.  none
10.  lines l and t

Proof review sheet

8.  Statements                                      Reasons

AB parallel to EC;                            given

BC parallel to EF                              given

angle 7 congruent to angle 5            if line parallel, corr. angles congr.

angle 5 congruent to angle 4            if lines parallel, AIA congruent

angle 7 congruent to angle 4            substitution

9.

          Statements                                   Reasons

line g parallel to line h                           given

angle 1 congruent to angle 2                  given

angle 1 congruent to angle 3                 if lines parallel, corr. angles congruent

angle 2 congruent to angle 3                 substitution

line p parallel to line r                           if AEA congruent, then lines parallel

11.  

        Statements                                    Reasons

line g parallel to line h                          given

angle 1 and 4 are supplementary          given

angle 1 + angle 4 = 180                        def. of supplementary

angle 1 = angle 2                                  if lines parallel, AIA are congruent

angle 2 + angle 4 = 180                        substitution

angle 2 and 4 are supplementary          def. of supplementary

line p parallel to line r                          if SSI angles are supp., then lines parallel

Honors Geometry; 10/26

We continued our work with triangle proofs today by showing how to use congruent triangles to prove other things.  The other things involved corresponding parts and/or parallel lines.  We went over 3 proofs together today before the students got started on their own work.  We will take some practice quizzes the next two days in preparation for our chapter 4 quiz on Monday, Oct. 31.

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

Geometry; 10/25

We started our review of chapter 3 today by going over a few proofs together in class.  Parallel line proofs will be what is on the test, so the students got a chance to practice some on their own.  We will go over another one tomorrow before doing the 2nd part of our review.


Assignment:  Chapter 3 review sheet

Honors Geometry; 10/25

We continued our work with congruent triangles today by taking a look at the first of the congruent triangle postulates.  We covered the SSS, ASA, and SAS postulates today by going over several diagrams and a few short proofs.  The students then got started on their homework assignment.


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

Geometry; 10/21

We revisited our inductive reasoning project today by taking a look at how to determine the angles in a polygon.  We went over how to calculate both interior and exterior angle sums, as well as using the formula that we derived during our project last week.  We went through a few examples together before the students got started on their assignment.


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

Geometry; 10/24

We continued our work with inductive reasoning by going over a wider variety of problems than we had introduced last week.  We pointed out the difference between inductive and deductive, as well as introducing the vocabulary term "conjecture."  We went through a few word problems together in addition to the number and shape problems that we had introduced last week.  The students then got started on their homework.


Assignment:  Inductive reasoning worksheet +  page 107;  CE 1-5;  p. 107-108;  WE  1-9, 15-17

Geometry; 10/21

We revisited our inductive reasoning project today by taking a look at how to determine the angles in a polygon.  We went over how to calculate both interior and exterior angle sums, as well as using the formula that we derived during our project last week.  We went through a few examples together before the students got started on their assignment.


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

Honors Geometry; 10/24

We got back our chapter 3 tests today in class and the students had a chance to go over them.  We then started the next chapter that deals with congruent triangles.  Our lesson today centered on how to determine if figures are congruent, and then if they are, then we learned how to write congruence statements.  We did this with drawings that were provided as well as drawings that were graphed.  We went over 3-4 examples together before the students got started on their homework.


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

Honors Geometry; 10/21

We turned in our review sheets today before taking the chapter 3 test in class.  The student had the period to work on the test.

Assignment:  extra credit puzzle option

Geometry; 10/20

We continued working with triangles today by demonstrating how to evaluate drawings with multiple overlapping triangles.  We went through the shortcut of exterior angles being the sum of the remote interior angles as well.  There were 4-5 sample problems the students tried on their own in the lesson before getting started on their assignment.


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

Honors Geometry; 10/20

We spent the first part of the period working through any questions that the students had on their review sheet.  We also had an entry task that involved writing one more proof before the test.  The students then got to work on an angle review puzzle that will be turned in tomorrow.

Assignment:  Angle review puzzle

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

Parallel Lines Review

1.  lines l and t
2.  lines j and k
3.  lines l and t
4.  lines j and k
5.  lines l and t
6.  none
7.  lines j and k
8.  lines j and k
9.  none
10.  lines l and t

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

Geometry; 10/19

Today's class focused on two things.  We finalized the rules for our polygon project.  We went over these together from the data we had collected.  The second focus was on a quick introduction to working with types of triangles (various vocabulary words) and also calculations with triangles.  Students used the work time today to either finish up their project calculations or get started on the triangle assignment for tonight.


Assignment:  classifying triangles packet

Honors Geometry; 10/19

We reviewed our final two parallel line proofs today in class before getting to work on a chapter 3 review sheet.  The bulk of the period was spent working on the review sheet in pairs.


Assignment:  Chapter 3 review sheet

Geometry; 10/18

We continued working on the inductive reasoning project that we started yesterday.  The goal of today was to use our data to plot two lines of best fit and then to be able to use those lines to come up with a rule for angles in polygons.  We worked with both the slope and point-slope line equations to fill out the calculation portion of the packet.

Assignment:  finish all the calculations in the inductive reasoning packet that you didn't finish in class.  This is due tomorrow.

Honors Geometry; 10/18

We reviewed some topics on the angles in polygons today before going on to our next lesson of inductive reasoning.  We had touched on this earlier last week with our work with polygons and the patterns of angles in them.  We further discussed how to do number problems, word problems, and drawing problems today by distinguishing between inductive and deductive reasoning.  The students got started on their homework during the last portion of the period.


Assignment:  Inductive reasoning worksheet +  page 107, CE #1-5;  page 107-108;  WE #1-17

Geometry; 10/17

The students got back their chapter 3 quizzes today and then we started on the 2nd half of the chapter.  Today's lesson focused on using inductive reasoning to determine the pattern that exists between different polygons.  The goal today was to generate a table of numbers that we could use to discover a pattern in the angles of a polygon.  We will work to graph these values tomorrow and answer some more calculation problems to determine a rule that we can use.

Assignment:  none

Honors Geometry; 10/17

We continued working with triangles today by expanding our study to all polygons.  We went over the two rules that were generated last week in our inductive reasoning project by looking at the interior and exterior angles of a polygon.  We went through 4-5 examples of these types of problems before the students got started on their assignment.


Assignment:  section 3-5;  page 103;  CE #1-6;  page 104-105;  WE   #1-17  (skip #7), 21, 22

Geometry; 10/14

We turned in our chapter 3 quiz review sheet to start off the period and then the students got started on their chapter 3 quiz.  They had the period to work on it.

Assignment:  extra credit puzzle option

Honors Geometry; 10/14

We turned in our Inductive Reasoning Project today and then started on the next topic:  working with the interior and exterior angles of triangles.  We went over several vocabulary words today in terms of the way triangles are classified, as well as demonstrating how to do some calculation type problems involving triangles.  The students then got started on the assignment.


Assignment:  section 3-4;  page 97-99;  WE  1-24, 26, 28, 30

Geometry; 10/13

Today's class was spent reviewing for the chapter 3 quiz tomorrow.  We went over a couple of proofs and some questions involving calculations with parallel lines.  We also reviewed the meaning of several vocab words and how they relate to parallel lines.  The rest of the period was spent working on the review assignment.  The answers to the review assignment appear below.

Assignment:  Chapter 3 quiz review WS

Chapter 3 quiz tomorrow



Properties of Parallel Lines

1.  If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.
2.  If a line is perpendicular to one of 2 parallel lines, then it is perpendicular to the other also.
3.  AIA
4.  corresponding
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

             1.                                                        1.  Given
             2.                                                        2.  def. of angle bisector
             3.   angle 1 congruent to angle 2        3.
             4.                                                        4.  transitive / substitution
             5.                                                        5.  If AIA congruent, then lines parallel


Angle calculation problems

19.  x = 4
20.  x = 7
21.  x = 8
22.  x = -7
23.  x = 9
24.  x = 5
25.  x = -6;  angles = 90
26.  x = 4;  angles = 85, 95
27.  x = 10;  angles = 60
28.  x = -9;  angles = 80, 100

Honors Geometry; 10/13

We continued working on our inductive reasoning project today in class.  The students worked to finish up their graphs and then answer the calculation questions.

Assignment:  finish Inductive Reasoning Project;  due tomorrow

Geometry; 10/12

We continued our work with parallel lines today by going over ways in which to prove lines are parallel.  We demonstrated a couple of proofs together using corr. angles, AIA angles, and SSI angles.  We then worked on how to decipher drawings to determine if lines are parallel.  The students then got started on their homework to wrap up the period.


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

Honors Geometry; 10/12

We returned the chapter 3 quiz today and went over a few questions together on it.  We then started an inductive reasoning project that involves discovering some patterns in polygon angles.  We will discover the pattern, graph the results, and then determine the final rule that we can use as we move on through the latter half of the chapter.


Homework:  none!

Honors Geometry; 10/11

We collected our review sheets for the chapter 3 quiz today before taking the chapter 3 quiz in class.  The students had the period to work on the quiz.


Assignment:  extra credit puzzle option

Geometry; 10/10

We got our tests back today and then went over some homework questions as well.  We then continued working on parallel lines and the properties of the angles they involve.  The three theorems we introduced involved corresponding angles, alternate interior angles, and same side interior angles.  We went through a few different calculation problems with these ideas before getting started on the homework assignment.


Assignment:  parallel lines worksheet +  page 80-81;  WE  1-9

Honors Geometry; 10/10

We went over the parallel line proofs worksheet today to start class.  There will be a couple of proofs on the quiz tomorrow.  We then spent some time reviewing a few key concepts from the first part of the chapter before getting started on the review assignment.

Assignment:  Chapter 3 quiz review sheet


Properties of Parallel Lines

1.  If 2 parallel planes are cut by a third plane, then the lines of intersection are parallel.
2.  If a line is perpendicular to one of 2 parallel lines, then it is perpendicular to the other also.
3.  AIA
4.  corresponding
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

             1.                                                        1.  Given
             2.                                                        2.  def. of angle bisector
             3.   angle 1 congruent to angle 2        3.
             4.                                                        4.  transitive / substitution
             5.                                                        5.  If AIA congruent, then lines parallel

Geometry; 10/7

We began chapter 3 today by taking a look at some of the figures and vocabulary words that go along with parallel lines.  The three types of angle pairs that we introduced were corresponding angles, alternate interior angles, and same side interior angles.  These angle pair types all need to be recognized from drawings, as we will be using these angles in various types of proofs and calculations to come in this chapter.  The homework is largely getting used to identifying these types of angle pairs in drawings.


Assignment:  section 3-1;  page 75;  CE  #2-14 all;  page 76;  WE  #1-17 all

Honors Geometry; 10/7

We continued to work with parallel line proofs today by going over our homework and then starting a proof worksheet together.  We went over 2-3 as a group and then the students began working on the proof worksheet on their own.

Assignment:  Parallel Line proofs worksheet

Geometry; 10/6

We answered a few questions on the review sheet to start the period and then turned both the review sheet and the entry tasks for chapter 2 in.  The students then spent the rest of the period taking the chapter 2 test.

Assignment:  extra credit puzzle option

Honors Geometry; 10/6

We continued our work with parallel lines today by using the knowledge about angle pairs that we have been developing to prove that lines are parallel.  We went through a drawing recognition example, as well as a few sample proofs before the students got started on their assignment.


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

Geometry; 10/5

We continued to work on proof writing today with two more examples of complete proofs.  After these, the students tried one on their own before getting started on the review sheet.  The last half of the period was spent working on the review sheet and getting feedback on how they were doing.  The answers to the review sheet will be posted on this sight later on this evening.


Assignment:  Chapter 2 Review Sheet

Chapter 2 Test is tomorrow


Answers to review sheet

Honors Geometry; 10/5

We continued our study of parallel lines today by taking a look at some of the properties of the angles pairs found in parallel lines.  We worked with corresponding angles (congruent), alternate interior angles (congruent) and same side interior angles (supplemental) with small proofs to show how calculation problems can be carried out given parallel lines.  We then did a few larger calculations together before getting started on the homework.

Assignment:  section 3-2;  page 81-82;  WE  #1-21 all

Geometry; 10/4

We continued working on our proof writing skills today in class by going over two more complete 2-column proofs together.  Being able to identify both the reasons and the statements in these proofs continues to be the focus of what we are trying to do.  We started the homework together by doing one of the proof problems and then the students got to work on their assignment.


Assignment:  section 2-6;  page 62;  CE 8, 10;  page 63;  WE 1-15 all;  page 65;  #2-7

Honors Geometry; 10/4

The students got back their chapter 2 test today and turned in any extra credit puzzles that they may have completed.  We then started on the next chapter that deals largely with parallel lines.  Today's lesson focused mostly on the symbols and angle pair positions that are associated with parallel lines.  We went through several examples together to show the students the patterns of how these angle pairs work.  They then got started on their assignment at the end of the period.


Assignment:  section 3-1;  page 75;  CE  2-10 all;   page 76-77;  WE  #1-17 all, 22-29 all

Geometry; 10/3

We continued working on how to write proofs today.  The vocab word today that we used was perpendicular.  We went through how to use 90 degrees/right angles in proofs to show perpendicular lines, as well as working with congruent and complementary angles.  We went over a few calculations together, as well as 3 short proofs to illustrate how these reasons can be used to prove various statements.  The students then got started on their assignment.


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

Honors Geometry; 10/3

We turned in the two review sheets for Chapter 2 and took a few questions on them to start the period.  The students then spent the rest of the period taking the chapter 2 test.


Assignment:  none;  extra credit puzzle option