Geometry; 9/30

Today's class periods were shortened due to the all-school assembly.  The students got their chapter 2 quizzes back and then we went over their homework from last night.  Today's lesson focused on a few more types of angle pair calculation problems, as we went through 2 together and then the students did 2 on their own.  They then got started on their homework.


Assignment:  Angle Pairs worksheet

Honors Geometry; 9/30

We had a shortened period today due to our first all school assembly.  We spent our time going over the chapter 2 review sheet today and answered any questions that came up.  We also went through one more proof together before getting started on the final review for the test on Monday.  The answers to this second review will be posted on this blog on Sunday afternoon.


Assignment:  Ch. 2 Review WS #2;  page 42;  WE 14;  page 65;  Self Test 2  #9


Answers to chapter 2 review sheet

1.  C
2.  E
3.  G
4.  F
5.  K
6.  L
7.  J
8.  D
9.  H
10.  M
11.  E
12.  G
13.  B
14.  P
15.  F
16.  D
17.  angle ABF
18.  angle ABH and angle EBC
19.  angle BEC and angle CED
20.  25

page 42 proof;  #14

1.  m angle SRT = m angle STR                        1.  given
2.  m angle 1 + m angle 3 = m angle SRT
     m angle 2 + m angle 4 = m angle STR         2.  angle addition postulate
3.  m<1 + m<3 = m<2 + m<4                            3.  substitution property
4.  m<3 = m<4                                                   4.  given
5.  m<1 = m<2                                                   5.  subtraction property =


page 65 proof;  #9

1.  <1 is supplemental to <3                               1.  given
     <2 is supplemental to <3
2.  m<1 + m<3 = 180                                          2.  definition of supplemental
3.  m<2 + m<3 = 180                                          3.  definition of supplemental
4.  m<1 + m<3 = m<2 + m<3                             4.  substitution / transitive
5.  m<3 = m<3                                                    5.  reflexive
6.  m<1 = m<2                                                    6.  subtraction prop. =
7.  angle 1 congruent to angle 2                         7.  definition of congruence
8.  line J is perpendicular to line K                    8.  if 2 lines form congruent
                                                                             adjacent angles, then lines are
                                                                             perpendicular

Geometry; 9/29

We continued our work with proofs and various vocab words today.  Today's lesson focused on three specific types of angle pairs:  complementary, supplementary, and vertical angles.  The numbers 90 and 180 cropped up again, and we showed how to work with these angle pairs with both proof statements and angle calculation problems.  Several of the problem types are mental math, so the homework includes several mental math problems for the students to work on.


Assignment:  section 2-4;  page 51-52;  CE  1-19 all;   page 52-53;  WE  1-21 all, 23, 24, 26

Honors Geometry; 9/29

We went over the homework today in class before getting started on our review session.  There were two more full proofs that we went over today as a group.  One dealt with some shortcuts using theorems, and this was the first time that the students had seen that in a proof.  The remaining part of the period the students spent working on their review sheet for the test.  We will go over this and answer any questions they may have tomorrow before working on the second review for Monday's test.


Assignment:  Chapter 2 review sheet #1

Geometry; 9/28

We spent the first part of the period taking any questions that the students had on the review sheet from yesterday.  I went over the proof answers with them together before turning the review sheet in.  The students then spent the rest of the period working on the chapter 2 quiz.

Assignment:  extra credit puzzle option

Honors Geometry; 9/28

We spent today talking about how to build a proof from start to finish.  The goal of this chapter is to be able to write proofs with only the drawing, the given, and the prove statement provided.  For much of the chapter we have been working with proofs in which all the statements are already written in.  We will spend the next couple of days working on proofs where both columns are blank and we fill them in completely.  We went over 3 together in class before the students got started on their assignment.


Assignment:  section 2-6;  page 63-64;  WE  #1-17 all, 19, 20

Geometry; 9/27

We answered some homework questions together and then spent some time working through a few major topics that will show up on the quiz tomorrow.  How to work with conditional statements (and the key words and phrases), how to write algebra proofs, and how to write geometric proofs were all skills that were reviewed.  The students then got started on the task of going through the chapter quiz review sheet.   Chapter 2 quiz is tomorrow.


Assignment:  Chapter 2 Quiz review


Review Sheet answers

Using Deductive Reasoning

1.  hypothesis:  line AB intersects line CD at X
     conclusion:  A, X, and C are coplanar
2.  Hypothesis:  I finish my homework
     conclusion:  I can ride my bicycle
3.  initial statement:  false
     Converse:  If M is midpoint of segment AB, then AM = MB;  converse is true
4.  transitive prop. =
5.  reflexive prop. =
6.  substitution prop. =
7.  symmetric prop. =
8.  addition prop. =
9.  angle bisector theorem
10.  segment addition postulate
11.  angle addition postulate
12.  midpoint theorem
13.  definition of angle bisector

Algebra proof #5                                                          

-3(x + 2) = 16 - x            given                                    
-3x - 6 = 16 - x               distributive prop                  
-6 = 16 + 2x                    addition prop. =                  
-22 = 2x                          subtraction prop. =              
-11 = x                            division prop. =                  

 Algebra proof  #7

6(x - 6) = x(16 - 7)     given
6x - 36 = 16x - 7x      distributive prop.
6x - 36 = 9x                combine like terms
-36 = 3x                       subtraction prop. =
-12 = x                         division prop. =


Properties of Algebra

1.  addition prop. =
2.  division prop. =
3.  multiplication prop. =
4.  subtraction prop. =
5.  division prop. =
6.  distributive prop.
7.  transitive prop. =
8.  symmetric prop. =
9.  addition prop. =
10.  transitive prop. =
11.  subtraction prop. =
12.  skip
13.  skip
14.   proof
           1.  given
           2.  reflexive
           3.  addition prop. =
           4.  segment addition postulate
           5.  transitive / substitution

Proving Theorems

1.  def. of midpoint
2.  def. of angle bisector
3.  midpoint theorem
4.  angle bisector theorem
5.  midpoint theorem
6.  segment addition postulate
7.  angle addition postulate
8.  angle addition postulate
9.  def. of segment bisector
10.  55
11.  65
12.  80
13.  9
14.  8
15.  4.5
16.  3.5
17.  items in a proof
        1.  given                2.  word definitions      
        3.  postulates         4.  theorems

Practice Proofs

1.  given
2.  def. of midpoint
3.  definition of congruence
4.  segment addition postulate
5.  substitution
6.  combine like terms / simplify
7.  division prop. =
8.  substitution prop. =


1.  given
2.  angle addition postulate
3.  substitution prop. =
4.  angle addition postulate
5.  transitive prop. / substitution prop.

Honors Geometry; 9/27

We continued our work with how to write proofs today by going over how to include perpendicular and complementary into our word definitions.  We illustrated 3 different proofs today that dealt with how to use these terms in proofs, as well as a couple of calculations dealing with perpendicular lines.   All of these terms continue to add to our repertoire of things to use when writing a proof.  The students then got started on their assignment at the end of the period.


Assignment:  section 2-5;  page 58-60;  WE  #1-25 all,  28

Geometry; 9/26

We spent some more time today going over how to work with proofs.  We demonstrated what to do with word definitions, drawings, and theorems in a proof.  We went through 2 proofs together before getting started on the homework.  We went through the proof for the midpoint theorem and the proof for the angle bisector theorem.


Assignment:  section 2-3;  page 45;  CE  #1-10 all;    page 46;  WE  #1-14 all

Honors Geometry; 9/26

We returned our chapter 2 quiz this morning and went over a few of the questions that were most often missed.  We then went through the lesson today that focused on how to use special angle pairs in both proofs and calculations.  The angle pairs we introduced were complementary, supplementary, and vertical angles.  We went through a few examples to show how to use these angle pairs before getting started on the assignment.


Assignment:  section 2-4;  page 52-54;  WE  #1-33 ;  skip the multiples of 3

Geometry; 9/23

We continued working on proofs today, going over our algebra proofs and introducing how to work with geometric proofs.  The importance of the drawings and vocabulary words were emphasized as we went through 3 proofs together before getting started on the assignment.


Assignment:  section 2-2;  page 41;  WE  4-10 all;  page 40;  CE  #1-10 all

Honors Geometry; 9/23

We turned in our chapter 2 quiz review to start the period and then spent the rest of the time taking the chapter 2 quiz.  The students had the period to work on it.

Assignment:  Extra credit puzzle option

Honors Geometry; 9/22

We did some reviewing of the first part of chapter 2 today, going over the vocabulary words associated with deductive reasoning together, as well as going through an algebra proof and a geometry proof together.  The students then spent the majority of the period working on the review sheet for the quiz.  I will post the answers to the review sheet on this site later this afternoon so you can check your work.

Quiz on chapter 2  (section 2.1 to 2.3) tomorrow.


Assignment:  Chapter 2 review sheet


Review Sheet Answers:


If-Then Statements;  Converses

1.  a. 2x - 8 = 26      b.  x = 17
2.  a.  it is raining    b.  the grass is wet
3.  If m angle SRA = m angle ART, then ray RA bisects angle SRT,;    false
4.  If a number is divisible by 5, then it is divisible by 10;   false
5.  false:    if x > 8, then x squared > 64;  true
6.  true;      If angle 1 is obtuse, then m angle 1 = 135;   false
7.  If (x - 1)(x + 8) = 0, then x =1 or x= -8
     If x = 1 or x = -8, then (x - 1)(x + 8) = 0
8.  If the measures of two angles are =, then the angles are congruent
     If two angles are congruent, then their measures are equal.
9.  A drawing with three points in a plane that are non collinear.

Properties from Algebra

1.  Addition property of =
2.  division prop. of =
3.  multiplication prop. of =
4.  subtraction prop. of =
5.  division prop. of =
6.  distributive prop. =
7.  transitive property
8.  symmetric prop. =
9.  addition prop. =
10.  transitive prop.
11.  subtraction prop. =
12.  subtraction prop. =
13.  addition prop. =
14.  proof steps
        1.  given
        2.  reflexive prop. =
        3.  addition prop. =
        4.  segment addition postulate
        5.  substitution property / transitive

Proving Theorems

1.  def. of midpoint
2.  def. of angle bisector
3.  midpoint theorem
4.  angle bisector theorem
5.  midpoint theorem
6.  segment addition postulate
7.  angle addition postulate
8.  angle addition postulate
9.  def. of segment bisector /  def. of midpoint
10.  55
11.  65
12.  80
13.  9
14.  8
15.  4.5
16.  3.5
17.     given info;   word definitions;    postulates;    theorems


Algebra Proofs worksheet   (evens)

Geometry; 9/22

We entered the world of two-column proofs today!  This is a skill that we will be working on for the next 6 chapters, so we have just started the journey.  Today was spent on how to set up a proof and learning how to work out algebraic proofs.  We reviewed some algebraic properties to use before working through how to solve an equation and give a reason for each step.  We went through three together before the students then got started on their assignment.



Assignment:  Algebra Proofs worksheet

Geometry; 9/21

We started our discussion of deductive reasoning today by taking a look at how conditional (if...then) statements work.  We went over how the words hypothesis, conclusion, counterexample, converse, and biconditional all fit into how to work with these types of statements.  There were a few examples of each before the students got started on their homework.


Assignment:  section 2-1;  page 34;  CE  #1-11;  page 35;  WE  #1-22 all

Honors Geometry; 9/21

We continued working with proofs today, going over the ones in homework and then walking through 2 more as a class.  The two proofs today illustrated what a theorem is and how both the angle bisector theorem and the midpoint theorem can be proved.  There are important differences between a theorem and a definition, and we spent some time demonstrating that today before the students got started on their homework.


Assignment:  section 2-3;  page 45;  CE  #1-10;   page 46;  CE  #1-18

We will spend some time reviewing the first 3 sections of chapter 2 tomorrow in preparation for our chapter 2 quiz on Friday over sections 2-1 to 2-3 .

Geometry; 9/20

We introduced the topic of deductive reasoning today through a video clip and through the use of some logic puzzles.  We went over the importance of collecting facts and putting them together in a particular order to arrive at a correct answer.  We didn't do geometry today, but we practiced the type of thinking necessary in order to do geometry.  The students got started on their logic puzzle packet in class.


Assignment:  logic puzzle packet

Honors Geometry; 9/20

We continued our work with proofs today by going over how to work with geometric proofs in a variety of settings.  We went over 3-4 together before the students got started on their assignment.  We really focused on finding the segment addition postulate and the angle addition postulate in the drawings we were working with so that we could use them in the proof.

Assignment:  Section 2-2;  page 41-42;  WE  7-12 all

Geometry; 9/19

Today was the chapter 1 test in class.  We turned in our entry task sheets as well as the chapter 1 review sheet before passing out the test.  After the test, the students had the option to work on an extra credit puzzle if they chose to do so.


Assignment:  none;  extra credit option

Honors Geometry; 9/19

We continued our work with deductive reasoning today by working through the first 2-column proofs that the students have seen.  We began by using algebra to introduce the concept of two column proofs and how to use properties of numbers in solving them.  We then showed a couple of geometric proofs involving drawings and postulates that the students could begin to get familiar with.


Assignment:  section 2-2;  page 40;  CE  #1-12 all;     page 41;  WE  1-6 all

Geometry; 9/16

We spent time today in class going over the review worksheet and working through one more vocabulary activity to help solidify both the terms and drawings that go along with them.  The chapter 1 test in on Monday, Sept. 19

Assignment:  study the review sheet and get ready for your test

Honors Geometry; 9/16

The students got back their Chapter 1 Test today and were able to ask questions on certain ones that they missed.  We then got going on the next unit as we started our study of deductive reasoning.  We went through several vocabulary words that dealt with conditional states, hypotheses, conclusions, converses, and biconditionals.  Each term was explained and demonstrated before the students got started on their assignment.


Assignment:  section 2-1;  page 34;  CE  1-11 all;   page 35-36;  WE  1-30;  skip the multiples of 3

Geometry; 9/15

We continued to review the postulates and theorems from Chapter 1 today through a short partner reading activity and a quick practice quiz.  We'll do a couple more review activities tomorrow in getting ready for next Monday's test.  The remainder of the period was used to work on the review sheet for chapter 1.  We will go over it tomorrow and answer any questions the students have.


Assignment:  Chapter 1 Review Sheet

Honors Geometry; 9/15

We turned in the tissue box activity and our ch. 1 entry tasks before taking the chapter 1 test in class today.  The students had the period to take the test if they needed it.  They then had an extra credit puzzle option to work on afterwards.


Assignment:  extra credit puzzle option

Geometry; 9/14

We further explained the angle addition problems before going on with today's lesson.  We focused on the postulates and theorems that we have learned this chapter by modeling them with various objects as well as learning some specific wording for each one.  The students also made simple drawings to illustrate each one of these statements.  The last part of the period was spent working on the assignment.


Assignment:  Section 1-3/1-4 worksheet;  page 24;  CE 5-12 all;   page 25;  WE  5-12 all

Honors Geometry; 9/14

We went over our review sheet today to begin class and then answered any further questions the students had in terms of chapter 1.  The bulk of the period was spent working on another review, the tissue box activity.  This can be completed at home as well, yet students worked together to answer a series of questions about points, lines, planes, and space in reference to a tissue box.  The answers to the review portion of the activity appear below.


Test on Chapter 1 is tomorrow.


Assignment:  Tissue Box Review Activity


Test 3 answers:  Definitions and Postulates

1.  F
2.  F
3.  F
4.  T
5.  K
6.  infinite
7.  a.   line RQ
     b.  if two planes intersect, they intersect in exactly one line
8.  a.  exactly 1
     b.  through any 2 points, there is exactly 1 line
9.  a.  exactly 1
     b.  Through any 3 noncollinear points, there is exactly 1 plane
10.  EFGH
11.  BDHF
12.  CDHG
13.  ABFE
14.  AFGD,  ABCD,  BCGF
15.  through a line and a point not in a line, there is exactly 1 plane
16.  If 2 lines intersect, then exactly 1 plane contains them.
  

Geometry; 9/13

We continued working with angles today, but our focus was on how to use the angle addition postulate in working with angle calculation problems.  There were 4-5 sample problems that we went through together in order to see how drawings and different vocab words will dictate what type of equation is written down and solved.  After the lesson, the students got started on their homework assignment.


Assignment:  Angle Addition worksheet #2-20 evens;   page 21  WE  15-18;  p. 22   WE  30-34

Honors Geometry; 9/13

We continued with our practice of postulates and theorems today by reading through them to each other a few times and then taking a quick practice quiz on them.  Focusing in on the key words and determining which of them to fill blanks in with will be what the students encounter on the test.  The remainder of the period was used to begin work on our first review sheet for the Chapter 1 test.  We will go over this in class tomorrow, so answers will not be posted online.

Assignment:  Chapter 1 Review Sheet


Thursday, Sept. 15;  Chapter 1 Test

Geometry; 9/12

We got back the quizzes from Friday so that students could see how they did.  We then started the next section which dealt with angle notation and different types of drawings and angle vocabulary words.  We went over a few examples together before students got started on their homework.

Assignment:  section 1-4;  page 20;  CE  #1-25 all   (skip 13-16);  page 21;  WE  #1-24 all   (skip 15-18)

Honors Geometry; 9/12

Welcome to our first regular Monday of the school year!  We started the last section of the chapter today by going over 11 postulates and theorems that pertain to points, lines, and planes.  Each one of these statements involve some key terms as well as a simple drawing.  They will serve as a foundation for us to use as we move forward into the next unit of study.


Assignment:  section 1-5;  page 24;  CE  5-12 all;   page 25;  WE  3-16 all

Geometry; 9/9

We turned in our quiz review sheets at the start of the period before then taking the chapter 1 quiz.  The students had the period to work on the quiz.  There was an extra credit option for students at the end of the period if they chose to work on it.


Assignment:  Extra Credit Puzzle

Honors Geometry; 9/9

Happy Friday!

We continued with our work on the angle addition postulate today by going over homework and then demonstrating 3 additional ways of working problems with the angle addition postulate.  Each drawing is a little different, so the more drawings we see, the better we can get at the problems.

The students got started on their homework at the end of the period.


Assignment:  section 1-3/1-4 worksheet;   section 1-4;  CE  #28-38 all


Upcoming Test:  Chapter 1 Test on Thursday, Sept. 15

Geometry; 9/8

We continued practicing our drawings together by going through a couple more today to start the period.  We then went through 2-3 larger calculation problems together before getting started on the review sheet for the quiz tomorrow.  The students spent the majority of the period working on the review sheet.  Check this site later in the day for the answers to the review sheet so that the students can check their answers before tomorrow's quiz.


Assignment:  Chapter 1 Quiz review sheet

Honors Geometry; 9/8

We continued with our work on chapter 1 today by going over all the notation and symbols associated with angles.  We introduced several new drawings, as well as showed how calculation problems can be worked through using the angle addition postulate.  This is very similar to the segment addition postulate that we had used previously.  The students got started on their assignment the last part of the period.


Assignment:  section 1-4;  page 21-22;  WE  #1-34;  skip every multiple of 3

Geometry; 9/7

We continued our work with graphing skills today by linking midpoints on the graph to the midpoint formula.  These types of problems can be solved using either a graph or a formula, but students need to be able to use both.  There were 4-5 examples that we went over together before the students got started on their assignment.

Assignment:  section 13-5;  page 545-546;  WE  #1-11 all  (skip # 4 and 6)
                       section 1-3;  page 15-16;  WE  #32-40 evens

Chapter 1 Quiz is this Friday, Sept. 9

Honors Geometry; 9/7

We started off the period today by answering any last minute questions that the students may have had about their review sheet.  Once this was done, we took the chapter 1 quiz in class.  The students had the period to work on it, and then had the option of working on an extra credit puzzle afterwards if they chose to.

Assignment:  none;  extra credit option available

Geometry; 9/6

Welcome back from the long weekend!  We spent today's lesson focusing on the segment addition postulate again and going over how the distance of segments can also be found using some algebra graphing skills.  We showed that using points on a coordinate grid can be a useful way to determine the distance between two points.  We made use of the pythagorean theorem and some skills in working with radicals to complete these problems.

Assignment:  section 13-1;  page 525;  CE  #4-9 all;    page 526;  WE  #1-10 all

Honors Geometry; 9/6

Welcome back from the long weekend!  We spent today answering some homework questions about the segment addition postulate, as well as going over a few more calculation problems together that use this important idea.  The rest of the time was spent working on the review sheet for the quiz tomorrow.  There is a key list of vocab words that are on the back of the review sheet that is important to know for the quiz tomorrow.   Check back at this site later in the day and you will be able to check your work.


Assignment:  Chapter 1 quiz review sheet

Geometry; 9/2

We spent today continuing on with geometric figures  (rays, segments, angles, opposite rays) and symbols.  We also did our first calculations by working with the segment addition postulate and writing out algebra equations from drawings.  We went over a few examples of these together before getting started on the assignment.

Assignment:  section 1-3;  page 15-16;  WE  1-30 all;  31-39 odd


Chapter 1 Quiz is Friday of next week;  Sept. 9

Honors Geometry; 9/2

We spent today continuing on with geometric figures  (rays, segments, angles, opposite rays) and symbols.  We also did our first calculations by working with the segment addition postulate and writing out algebra equations from drawings.  We went over a few examples of these together before getting started on the assignment.

Assignment:  section 1-3;  page 15-16;  WE  1-46;  skip the multiples of three


Chapter 1 Quiz is Wednesday of next week;  Sept. 7

Geometry; 9/1

Happy September!    We continued our work with drawing figures in geometry today by going over what 2 intersecting planes look like.  We reviewed our work from yesterday with an activity that involved describing and drawing different figures to partners.  The students spent the bulk of the period working on this activity.

Assignment:  section 1-2;  page 7;  CE  #1-20

Honors Geometry; 9/1

Happy September!    We continued our work with drawing figures in geometry today by going over what 2 intersecting planes look like.  We reviewed our work from yesterday with an activity that involved describing and drawing different figures to partners.  The students spent the bulk of the period working on this activity.

Assignment:  section 1-2;  page 7;  CE  #1-20