Download Geometry Fall 2013 Lesson 017 _Using postulates and theorems to

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Lesson Plan #17
Class: Geometry
Date: Tuesday October 8th, 2013
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 7and 8
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 reason in the proof below
Given:
Prove:
3
Statements
1.
2.
4.
5.
6.
7.
8.
9.
10.
1
Reasons
1.Given
2.Given
3.Given
4. Definition of complementary angles (3)
5.
6. Transitive property of equality (4,5)
7.
8. Substitution Postulate (6,7)
9.
10.
or
11.
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
4
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:
Statements
1.
2.
3.
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
Statements
1.
2.
and
intersect at E
3. <BEC is the supplement of <AEC; <AED is the supplement
of <AEC
4. <BEC <AED

A
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
Reasons
3
Assignment #4:
4
Sample Proof:
Statements
1.
Reasons
1. Given
2.
2. Given
3. m< r= m<s
4.
bisects
3. Definition of congruent angles (2)
4. Given
5.
5. Given
bisects
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. m<CBF + m<y + m<s = 180
7. Same as reason 6 (1)
8. m<CBE + m<x + m<r = m<CB F+ m<y + m<s
8. Transitive Property of Equality (6, 7)
9. m<r = m<s
9. Definition of congruent angles (2)
10. m<CBE + m<x + m<s = m<CBF + m<y + m<s 10. Substitution Postulate (8,9)
11. m<s = m<s
11. Reflexive Property of Equality
12. m<CBE + m<x = m<CBF + m<y
12. Subtraction Postulate (10,11)
13. <CBE is congruent to <x
13. Definition of an angle bisector (4)
14. m<CBE = m<x
14. Definition of congruent angles (13)
15. <CBF is congruent to <y
15. Definition of an angle bisector (5)
16. m<CBF = m<y
16. Definition of congruent angles
17. m<x + m<x = m<y + m<y
17. Substitution Postulate (12, 14, 16)
Or 2m<x = 2m<y
18.m<x = m<y
18. Division Postulate (17)
19.
19. Definition of congruent angles (18)
<x is congruent to <y
6. m<CBE + m<x + m<r = 180