1. 2.6 Prove Statements About Segments and Angles

2. Vocab Proof: a logical argument used to show something is true
Two column proof: a numbered statement and corresponding reason that shows an argument in a logical order
Theorem: a statement that can be proven

3. Theorems

4. Two column proof

5. Given: <1 and < 2 are complementary
Prove: m<2 = 16
Statement Reason
m<2 = 74
<1 and <2 are complementary
m<1 + m<2 = 90
m<1+ 74 = 90
M<1 = 16
Given
Given
Def complementary angles
Substitution
Subtraction

6. Given:
<1 and <2 are supplementary
m<2 = 145
Prove m<1 = 35
<1 and <2 are supplementary
m<2 = 145
m<1 + m<2 = 180
m< = 180
m<1 = 35
Given
Given
Def of supplementary angles
Substitution
Subtraction

7. Given:
m<N = 42
m<L = 116
Prove:
m<M = 22
m<L + m<M + m<N = 180
m<N = 42
m<L = 116
42 + m<M = 180
m<M = 180
m<M = 22
The sum of the measures of the angles of a triangle is 180
Given
Given
Substitution
Combine like terms
Subtraction