Vertical Angles Example:
∠2 and ∠4 are vertical angles
∠1 and ∠3 are vertical angles
Properties:
Vertical angles are always congruent
Vertical angles always have the same measure
Vertical Angles Proof Number 1:
Two-Column Proof
Given: a || b and t with transversal t
Prove: ∠2 and ∠4 are congruent
| Statement | Reason |
|---|---|
| a || b and t with transversal t | Given |
| ∠1 + ∠2 = 180° | Linear pair of angles |
| ∠1 + ∠4 = 180° | Linear pair of angles |
| ∠1 + ∠2 = ∠1 + ∠4 | Transitive Property |
| ∠2 = ∠4 | Equality Property |
Vertical Angles Proof Number 2:
Two-Column Proof
Given: a || b and t with transversal t
Prove: ∠1 and ∠3 are congruent
| Statement | Reason |
|---|---|
| a || b and t with transversal t | Given |
| ∠2 + ∠1 = 180° | Linear pair of angles |
| ∠2 + ∠3 = 180° | Linear pair of angles |
| ∠2 + ∠1 = ∠2 + ∠3 | Transitive Property |
| ∠1 = ∠3 | Equality Property |
Final Answer
Vertical angles are always congruent
Vertical angles always have the same measure
Vertical angles always have the same measure
