Geometry; 9/28

We took the first few minutes of class to answer any remaining questions on the chapter 2 quiz review sheet.  The students then turned in the reviews and took the rest of the period to complete the chapter 2 quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 9/28

We continued our work with how to write geometric proofs.  We now have several more tools to use in this process, so the topic today was planning a proof and how to put them together based on the information we have.  We went through 3-4 more proofs together before getting started on the assignment......more practice proofs!

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

Geometry; 9/27

We spent time today in class reviewing the different types of questions that will appear on tomorrows quiz.  From algebra proofs to geometric proofs to conditional and biconditional statements, the students had chances to practice each skill in class before getting started on the review sheet.  Chapter 2 quiz is tomorrow.

Assignment:  Chapter 2 Quiz review sheet


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

Honors Geometry; 9/27

We continued our work with proofs today by adding the topic of perpendicular lines to the mix.  We went over how to incorporate the definition of perpendicular lines into both calculation problems and proofs.  There were 3-4 examples we went over together before the students got started on their homework assignment.


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

Geometry; 9/26

We continued to work on geometric proofs today by taking a look at how to incorporate the midpoint theorem and the angle bisector theorem into our work.  Both of these theorems were demonstrated together before the students got started on their assignment.


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

Honors Geometry; 9/26

The students got back their chapter 2 quiz today and were able to ask any questions that they may have had.  We also moved on in our study of proofs to take a look at special pairs of angles.  We went over complementary, supplementary, and vertical angles today.  We demonstrated how to do both calculation problems and proofs using these pairs of angles.

Assignment:  section 2-4;  page 52-54;  WE  1-33 all

Geometry; 9/25

We continued our work with writing geometric proofs.  We went through 3 more today together before the students got started on their assignment.  Our focus is on recognizing both the segment addition and the angle addition postulate in drawings.


Assignment:  Section 2-2;  page 41-42;  WE #1-10

Honors Geometry; 9/25

The students turned in their chapter 2 quiz review sheets to start the period.  We went over a few questions together.  The rest of the period was then devoted to taking the chapter 2 quiz.


Assignment:  extra credit puzzle option

Geometry; 9/22

We went over a couple of algebra proofs to start the class before getting started.  The main topic today was to demonstrate how to write and reason through a geometric proof.  We went through two together before getting started on the homework as a class.

Assignment:  section 2-2;  page 40;  CE  #1-12

Honors Geometry; 9/22

We spent time in class today reviewing the proof worksheet from last nights homework and going over a few more proofs together in preparation for Monday's quiz.  Once we did this, the students got started on their chapter 2 quiz review worksheet.


Assignment:  Chapter 2 quiz review


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; 9/21

We continued our work with deductive reasoning in geometry today by taking a look at what biconditional statements in geometry are and how they are formed from two different statements.  We then explained how to use the various properties of algebra to work through algebra proofs.  The two column format with statements and reasons was demonstrated a few times together before the students got started on their assignment.


Assignment:  Algebra proofs worksheet

Honors Geometry; 9/21

We continued our work with proofs today by taking a look at three more proofs together involving the segment addition and the angle addition postulate.  The students then got to work on their assignment involving both filling in partially complete proofs as well as writing two complete proofs.


Assignment:  Proof practice worksheet ;  page 41;  WE 13, 14

Geometry; 9/20

We continued our work with deductive reasoning today by taking a look at the different ways that conditional statements can be written.  These if....then statements can also be evaluated as true or false, and then rewritten as a converse if the need arises.  We practiced each one of these skills together before getting started on the assignment.

Assignment:  conditional statements worksheet  +  page 34;  CE 8-11

Honors Geometry; 9/20

We continued our work with proofs in geometry today by proving the first two theorems that we will be working with:  the midpoint theorem and the angle bisector theorem.  Both of these concepts are ones that we will use throughout the year, and we use their initial proof to further demonstrate how to work with two column proofs and fitting various facts, word definitions, and postulates into the overall proof table.


Assignment:  Section 2-3;  page 46-47;  WE 1-17

Geometry; 9/19

We started our study of chapter 2 today by taking a look at how deductive reasoning works and the importance of organizing facts is when deducing conclusions.  A quick comparison was made with inductive reasoning to highlight the differences between the two different types of thinking.  The students then worked on their logic skills with a variety of logic puzzles to solve deductively.


Assignment:  Logic Puzzle Packet

Honors Geometry; 9/19

We continued our work with proofs today by going over 3 more geometric proofs and how to work with various kinds of facts.  Right now our main skill is working with word definitions, segment addition postulate, and the angle addition postulate.  After going over the three proofs together, the students then got started on their assignment.


Assignment:  section 2-2;  page 41-42;  WE 7-12

Geometry; 9/18

We answered a few questions together before getting started on the test.  The students turned in their chapter 1 entry tasks and their chapter 1 reviews to start the period.  The rest of the period was then spent working on the the chapter 1 test.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 9/18

We started the process today of learning how to do proofs in geometry.    We went over several properties of algebra that the students are familiar with and how to use these in writing an algebra proof.  We went over a couple of algebra proofs together.  I then introduced a geometric proof and how to use a drawing to complete one.  The students then got started on their assignment.

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

Geometry; 9/15

We spent time in class today going through 4 more sample types of problems that will be on the test on Monday.  The distance and midpoint formulas were reviewed, as well as how to handle problems involving the segment addition and the angle addition postulate.  The students then spent the last part of the period working on their chapter 1 review sheet.


Assignment:  Chapter 1 Review sheet

Chapter 1 Test on Monday, Sept. 18


Answers to Review Sheet

Points, Lines, Planes, and Angles

1.  E
2.  C
3.  angle AEB or 180 degrees
4.  12
5.  -1
6.  J
7.  3
8.  ray LK or ray LJ
9.  angle AHE
10.  angle AHC
11.  obtuse
12.  angle addition postulate
13.  def. of midpoint
14.  def. of angle bisector
15.  segment addition postulate
16.  ray HE and ray HB
17.  angle DHE and angle EHC
18.  ray HF
19.  angle DHE and angle EHC  or angle 2 and angle 3
20.  false
21.  true
22.  false
23.  true


Distance and Midpoint Formula Review Problems

1.  formula in notes
2.  radical 130 or 11.4
3.  formula in notes
4.  midpoint = (-7.5, 4.5)
5.  endpoint = (-13, 8)
6.  x = 5,  AB = 29,  BC = 27
7.  x = 3.57;   AT = 12.25;  TL = 15
8.  x = 8;  angle AQB = 40;  angle BQC = 40;  angle AQC = 80
9.  x = 5;  angle LIK = 20;  angle JIL = 110;  angle JIK = 90
10.  x = 3;  angle RAM = 140;  angle MAN = 40;  angle RAN = 180

Honors Geometry; 9/15

The students got their chapter 1 tests back and were able to ask about any questions that they had.  We then got started on chapter 2 today by taking a look at how deductive reasoning works in geometry.  We introduced several new vocab terms today :  if...then statement, converse, hypothesis, conclusion, counterexample, and biconditional statement.  All of these were demonstrated and used to solve various types of questions.  The students then got started on their homework assignment.


Assignment:  section 2-1;  page 34;  CE 1-11;    page 35;  WE 1-30  (skip multiples of 3)

Geometry; 9/14

We went over our homework and reviewed how to handle segment addition calculations.  We then went through two different activities to help us review the postulates and theorems that we have been working with.  After the activities the students then got started on their homework assignment.


Assignment:  vocab review sheet + self test 2;  page 29;  #1-12

Honors Geometry; 9/14

The students turned in their chapter 1 reviews and entry tasks today before taking the chapter 1 test.  The students used the entire period to take the test.

Assignment:  none;  extra credit puzzle option

Geometry; 9/13

We continued our work with chapter 1 today by going over all the important postulates and theorems that involve points, lines, and planes.  We used some physical models to do this, as well as some simple drawings and phrases.  The students then got started on their homework assignment.


Assignment:  section 1-5;  page 24;  CE 5-12;  pg. 25;  WE 5-12;  p. 22;  WE 30, 33, 34

Honors Geometry; 9/13

We spent time today going over the review sheet for chapter 1 and getting ready for the chapter 1 test (tomorrow).  We answered several questions from the review sheet to further explain any concepts the students asked about.  The students then got to work on a tissue box activity that reviewed various concepts with 3-D drawings and the postulates and theorems we have been working on this chapter.


Assignment:  Tissue Box Activity + Review Sheet #2


Definitions and Postulates Review Sheet Answers

1.  false
2.  false
3.  false
4.  true
5.  plane K
6.  infinite
7.  a.  line RQ
     b.  if 2 planes intersect, they intersect in exactly 1 line
8.  a.  exactly 1
     b.  through any two points, there is exactly one 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 on the line there is exactly one plane
16.  if two lines intersect, then exactly 1 plane contains both lines

Geometry; 9/12

The students got back their chapter 1 quiz today and they had a chance to go over any questions that they had.  We then continued our work with the angle addition postulate by going over 3-4 more problems together showing the different ways that angles can be combined.  The students then got started on their assignment the last part of the period.


Assignment:  Angle Addition worksheet

Honors Geometry; 9/12

We started our review today for the chapter 1 test.  We went over a postulate review activity together and took a quick practice quiz over the postulates and theorems.  The rest of the period the students then spent working on the review sheet for chapter 1.  We will go over this assignment tomorrow before working on another review activity.


Assignment:  Chapter 1 Review Sheet

Geometry; 9/11

We continued our study of the foundations of geometry today by going over the symbols and notation for several different types of angles.  We went over new vocab words and showed how to draw each one, as well as introducing how to work problems using the angle addition postulate.

Assignment:  section 1-4;  page 20;  CE 1-25;   page 21;  WE 1-18, 31, 32

Honors Geometry; 9/11

We introduced the concept of theorems today as we went over all the different postulates and theorems that are used with points lines and planes.  We reviewed some drawings, as well as observed some physical models of how the postulates and theorems play out in 3-dimensional space.


Assignment:  section 1-5;  page 25;  WE 1-17;  page 29;  Self Test #2;  #1-8 all

Geometry; 9/8

We answered a few questions from the review sheet today before turning it in and taking the chapter 1 quiz.  The students had the period to take the quiz.


Assignment:  none;  extra credit puzzle option

Honors Geometry; 9/8

We continued to work on how to identify angles in drawings today, and the specifics of how the angle addition postulate must be used.  We went over a couple more calculation problems together before getting started on the assignment.


Assignment:  section 1-4;  page 20;  CE 28-38  +  1-3/1-4 worksheet

Geometry; 9/7

We spent the first part of today reviewing the different vocab words we have learned to draw with a quick drawing quiz.  We then did one more distance and midpoint calculation together before getting started on the review sheet.  The bulk of the period was spent working on this in preparation for tomorrow's quiz.  Answers to the review sheet will be posted later on this afternoon.


Assignment:  Chapter 1 quiz review sheet


Answer key to review sheet

Vocab Review Sheet

1.  collinear
2.  length
3.  postulate, axiom
4.  equidistant
5.  coplanar
6.  midpoint
7.  point
8.  ray
9.  segment bisector
10.  line
11.  congruent segments
12.  space
13.  intersection
14.  opposite rays
15.  plane
16.  coordinate
17.  segment
18.  congruent


Some Basic Figures

1.  false
2.  true
3.  false
4.  true
5.  false
6.  false
7.  true
8.  true
9.  true
10.  false
11. unlimited
12.  2
13.  1
14.  drawing of a single vertical plane labeled with a capital C
15.  drawing of line h intersecting plane D at X.  part of line h should be dotted.
16.  drawing of two lines intersecting in the same plane;  no dotted lines here
17.  drawing of two planes intersecting in line XY


Exercises:

1.  line AB or line AC
2.  line BD
3.  point E or D
4.  line AB, line AC, or line BC
5.  point E
6-10.  drawings

Segments and Distance;  Angles

1.  8
2. 7
3. 10
4.  16
5.  point D
6.  points E and M
7.  point G
8.  -3
9.  ray DC
10.  segment CK or segment EM
11.  x = 3
12.  x = 1/2

Distance and Midpoint Practice Problems

1.  distance formula
2.  square root of 233 = 15.3
3.  square root of 149 = 12.2
4.  midpoint formula
5.  M = (-0.5, 6)
6.  a.  square root of 136 = 11.7
     b.  M = (1, 1)
     c.  endpoint T = (-14, -8)

Honors Geometry; 9/7

We passed back the chapter 1 quizzes today and the students had a chance to go over and ask about any mistakes they had made.  We then went on with the next topic in our chapter:  how to work and calculate with angles.  We went over several new vocab words dealing with different types of angles and how to draw them.  We then showed how the angle addition postulate works and related it to what we already studied with the segment addition postulate.

Assignment:  section 1-4;  page 20;  CE 17-25 all;   page 21;  WE 1-34  (skip multiples of 3)

Geometry; 9/6

The topic for today dealt with graphing again, but today we worked with finding the midpoint of a segment.  Just like with finding distance, there is both a graphical method and a method using a formula.  We went over both methods in class to make sure that students could handle either one.  We then showed how to determine endpoints using the midpoint of a segment.

Assignment:  page 545-546;  WE  #1-11 all;   page 15-16;  WE  32-40 evens

Honors Geometry; 9/6

We spent a few minutes answering questions from the review sheet today before taking the chapter 1 quiz in class.  After the quiz, the students could work on an extra credit option if they chose.

Assignment:  Chapter 1 Quiz;  extra credit option

Geometry; 9/5

We practiced a couple more calculation problems involving the segment addition postulate to begin the period.  We then went over how to determine the length of a segment that is graphed on a coordinate axes.  We used our graphing skills and the pythagorean theorem to come up with the distance formula and how to use it with two points.  The students practiced a few examples together before getting started on the homework.


Assignment:  page 525;  CE 4-9;  page 526;  WE 5-8;  page 14;  CE 1-12

Honors Geometry; 9/5

We spent some time today continuing to review the segment additional postulate and how it can be used to calculate various unknown quantities involving lengths.  We went over a couple of review problems together before getting started on the chapter 1 quiz review sheet.  The answers to this will be posted later on today in preparation for the quiz tomorrow on Chapter 1.


Assignment:  Chapter 1 Quiz review sheet

Answer key to review sheet

Some Basic Figures

1.  false
2.  true
3.  false
4.  true
5.  false
6.  false
7.  true
8.  true
9.  true
10.  false
11. unlimited
12.  2
13.  1
14.  drawing of a single vertical plane labeled with a capital C
15.  drawing of line h intersecting plane D at X.  part of line h should be dotted.
16.  drawing of two lines intersecting in the same plane;  no dotted lines here
17.  drawing of two planes intersecting in line XY

Points, Lines, and Planes

1.  answer will vary
2.  area I = area 2
3.  true
4.  false
5.  false
6.  true
7.  false
8.  true
9.  true
10.  false
11.  true
12.  true
13.  E
14.  F
15.  A
16.  H
17.  line EF, line AE, line EH
18.  plane BCDA
19.  plane CBFD and plane CDHG
20.  planes ABCD, AEHD, and DCGH
21.  drawing of two planes intersecting in line RS
22.  drawing of line AB in plane M.  Line AC should be partly dotted, as it intersects line AB at point A

Exercises:

1.  line AB or line AC
2.  line BD
3.  point E or D
4.  line AB, line AC, or line BC
5.  point E
6-10.  drawings

Segments and Distance;  Angles

1.  8
2. 7
3. 10
4.  16
5.  point D
6.  points E and M
7.  point G
8.  -3
9.  ray DC
10.  segment CK or segment EM
11.  x = 3
12.  x = 1/2

Geometry; 9/1

We continued to work on introducing various vocabulary words and symbols today in class.  Rays, segments, midpoint, bisect, and segment addition postulate were all topics that we demonstrated how to use in today's lesson.  We also worked on our first calculations using length in a variety of drawings.


Assignment:  section 1-3;  pp. 15-16;  WE 1-30 all;  31-39 odds

Honors Geometry; 9/1

We continued to work on introducing various vocabulary words and symbols today in class.  Rays, segments, midpoint, bisect, and segment addition postulate were all topics that we demonstrated how to use in today's lesson.  We also worked on our first calculations using length in a variety of drawings.


Assignment:  section 1-3;  pp. 15-16;  WE 1-46  (skip multiples of 3)