This document discusses deductive reasoning and proof. It provides an example proof that if two angles are vertical angles, then they are equal in measure. It uses the facts that the angles add up to 180 degrees, the transitive property, and the addition property of equality to prove the two angles are the same measure. It also gives another example to prove that if two angles are complementary to the same angle, then they are equal to each other.

1. Ch3.7_DeductiveReasoning.notebook October 07, 2011
Chapter 3.7
Deductive Reasoning
and Proof
Deductive Reasoning
Using rules and true statements
to prove an idea

2. Ch3.7_DeductiveReasoning.notebook October 07, 2011
RULES SHEET
Prove the Following
If two angles are vertical angles,
then they are equal in measure
3
2
1
Given: <1 and <2 are vertical angles
Prove: m<1 = m<3
STATEMENT REASON
<1 and <2 Given
are vertical angles
m<1 + m<2 = 1800 Angle addition
m<2 + m<3 = 1800
m<1 + m<2 = m<2 + m<3 Transitive Property
Addition Property
m<1 = m<3 of Equality

3. Ch3.7_DeductiveReasoning.notebook October 07, 2011
Prove the Following
If two angles are complementary to the same angle,
then they are equal to each other
Draw a diagram
1 3
2
<1 and <2 <2 and <3
are complementary are complementary
STATEMENT REASON
Worksheet
for practice