Download Geometry Fall 2012 Lesson 017 _Using postulates and theorems to

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Lesson Plan #17
Class: Geometry
Date: Wednesday October 10th, 2012
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, 8 and 9
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 complimentary 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
What theorem was just proven in the Do Now?
11. Definition of Congruent angels (10)
4
2
2
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
Given:
Prove:
B
C
E
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.
Statements
Reasons
3
Assignment #3:
Complete the proof below