2.6 Proving Angles Congruent
Date:
Goals:
• Prove theorems about angles
• Apply theorems about angles
Vertical Angles Theorem:
Example 1: Prove Vertical Angle Theorem
Complete the following proof.
A. Given: 1and 3 are vertical angles.
1
2
Prove: 1  3
Statement
1. 1and 3 are vertical angles.
2.
3.
1and 2 are supplementary
2and 3 are supplementary
m1  m2  180
m2  m3  180
4. m1  m2  m2  m3
5. m1  m3
6. 1  3
Reason
3
Example 2: Using Vertical Angles
Find the value of x in each of the following diagrams.
A.
B.
E
A
115
C x
B
D
D
Example 3: Using Vertical Angles in Proofs
Complete the following proof.
Prove: 2  4
Statement
1. 1 3
2. 3  2
3. 1 2
4. 1 4
5. 2  4
E
A
 6 x  18 
B
A. Given: 1 3
120
1
3
2
4
Reason
C
Congruent Supplements Theorem:
Congruent Complements Theorem:
Theorem 2-4:
Theorem 2-5: