Download Geometry Fall 2015 Lesson 017 _Using postulates and theorems to

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Lesson Plan #17
Class: Geometry
Date: Monday October 19th, 2015
Topic: Using postulates and definitions to prove statements in geometry
Aim: Students will be able to use postulates and definitions to prove statements in geometry?
HW #17:
Prove the conclusions in 7
Objectives:
Students will be able to use definitions, postulates and theorems to prove statements.
Note:
Below are the theorems we proved yesterday
 Theorem - If two angles are right angles, then they are congruent
 Theorem - If two angles are straight angles, then they are congruent
 Theorem - If two angles are complements of the same angle, then they are congruent
 Theorem - If two angles are supplements of the same angle, then they are congruent
Do Now: Fill in the missing reasons in the proof below
Given:
 1  2
 4 is complementary to  1
 3 is complementary to  2
3
4
1
Prove:
 4  3
Statements
Reasons
1.  1  2
2.  3 is complementary to  2
1.Given
2.Given
3.  4 is complementary to  1
4. m  4  m  1  90
5. m  3  m  2  90
6. m  4  m  1  m  3  m  2
7. m  1  m  2
8. m  4  m  2  m  3  m  2
9. m  2  m  2
10. m  4  m  2  m  2  m  3  m  2  m  2
or
3.Given
4. Definition of complementary angles (3)
5.
6. Transitive property of equality (4,5)
7.
8. Substitution Postulate (6,7)
9.
10.
11.
 4  3
m4m3
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
11. Definition of Congruent angles (10)
2
2
What theorem was just proven in the Do Now?
A similar proof can be provided for the following theorem:

If two angles are congruent, then their supplements are congruent.
Recall the definition of a linear pair: A linear pair of angles are two adjacent angles whose sum is a straight angle.
Assignment #1: Fill in the missing reason in the proof
1
2
Given:
<1 and <2 form a linear pair
Prove:
 1 is supplementary to angle  2
Statements
1.  1 and  2 form a linear pair
2.
3. m  1  m  2  180
4. <1 is supplementary to angle <2
Reasons
1. Given
2. Definition of a linear pair
3.
4. Definition of supplementary angles
Theorem: If two angles form a linear pair, they are supplementary
Assignment #2: Fill in the missing reason in the proof
B
Given:
C
E
Prove:
D
A
Statements
1.
2.
and
intersect at E
3. <BEC is the supplement of <AEC; <AED is the supplement
of <AEC
4. <BEC  <AED

Reasons
1. Given
2. Definition vertical angles
3. If two angles form a linear pair, they are supplementary
4.
Theorem – If two angles are vertical angles, then they are congruent.
Assignment #3:
Complete the proof below
Statements
ect
Reasons
1. CE bisects  ADB
1.
2.  ADE  BDE
2.
3. FDB and
3.
CDE intersect.
4.  BDE and  FDC are
vertical angles
5.  BDE  FDC
4.
6.
6. Transitive Property of congruence (2,5)
5.
3
Sample Proof:
Statements
1. ABC
2.  r  s
3. m  r  m  s
4. BE bisects  CBD
5. BF bisects  CBG
6. m  CBE  m  x  m  r  180
7. m  CBF  m  y  m  s  180
8. m  CBE  m  x  m  r  m  CBF  m  y  m  s
9. m  r  m  s
10. m  CBE  m  x  m  s  m  CBF  m  y  m  s
11. m  s  m  s
12. m  CBE  m  x  m  CBF  m  y
13.  CBE   x
14. m  CBE  m  x
15.  CBF  y
16. m  CBF  m  y
17. m  x  m  x  m  y  m  y
2m  x  2m  y
or
18. m  x  m  y
19.  x  y
Chapter Review:
Reasons
1. Given
2. Given
3. Definition of congruent angles (2)
4. Given
5. Given
6. Postulate – The sum of the degree measures
of all the angles on one side of a given line
whose common vertex is a given point on the
line is 180 (1)
7. Same as reason 6 (1)
8. Transitive Property of Equality (6, 7)
9. Definition of congruent angles (2)
10. Substitution Postulate (8,9)
11. Reflexive Property of Equality
12. Subtraction Postulate (10,11)
13. Definition of an angle bisector (4)
14. Definition of congruent angles (13)
15. Definition of an angle bisector (5)
16. Definition of congruent angles
17. Substitution Postulate (12, 14, 16)
18. Division Postulate (17)
19. Definition of congruent angles (18)
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