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HW- pg. 113 (1-5)
Ch. Test THURSDAY 10-10-13
www.westex.org HS, Teacher Website
10-4-13
Warm up—Geometry CPA
Determine whether each statement is true or
false. If false, give a counterexample.
1. If two angles are complementary, then they are
not congruent.
2. If two angles are congruent to the same angle,
then they are congruent to each other.
GOAL:
I will be able to:
1. write two-column proofs.
2. prove geometric theorems by using deductive
reasoning.
HW- pg. 113 (1-5)
Ch. Test THURSDAY 10-10-13
www.westex.org HS, Teacher Website
Name _________________________
Geometry CPA
2-6 Geometric Proof
GOAL:
I will be able to:
1. write two-column proofs.
2. prove geometric theorems by using deductive reasoning.
Date ________
When writing a proof, it is important to justify each logical step with a reason. You can use
symbols and abbreviations, but they must be clear enough so that anyone who reads your
proof will understand them.
Example 1: Writing Justifications
Write a justification for each step, given that
A and B are supplementary and mA = 45°.
STATEMENT
REASON
1. A and B are supplementary 1.
mA = 45°
2. mA + mB = 180°
2.
3. 45° + mB = 180°
3.
4. mB = 135°
4.
YOU TRY:
Write a justification for each step, given that
B is the midpoint of AC and AB  EF.
STATEMENT
REASON
1. B is the midpoint of AC.
1.
2. AB  BC
2.
3. AB  EF
3.
4. BC  EF
4.
A _______________ is any statement that you can prove. Once you have proven a theorem,
you can use it as a reason in later proofs.
Example 2: Linear Pair Theorem If two angles form a linear pair, then they are
supplementary.
Given: 1 and 2 are a linear pair
Prove: 1 and 2 are supplementary
Statements
1. 1 and 2 are a linear pair
2.
and
form a line.
Reasons
1.
2. Def. of linear pair
3. mABC = 180°
3.
4. m1 + m2 = mABC
4. Angle addition post.
5.
5. Subst. steps 3, 4
6. 1 and 2 are supplementary
6.
A geometric proof begins with Given and Prove statements, which restate the hypothesis and
conclusion of the conjecture. In a _________________ __________, you list the steps of
the proof in the left column. You write the matching reason for each step in the right column.
Example 3: Congruent Supplements Theorem
Given: 1 and 2 are supplementary, and 2 and 3 are supplementary.
Prove: 1  3
Example 4: Congruent Complements Theorem If two angles are
complementary to the same angle (or to two congruent angles), then the two
angles are congruent.
Given: ∠1 and ∠2 are complementary and ∠2 and ∠3 are complementary.
Prove: ∠1  ∠3
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.