Consecutive Interior Angles Example:
∠3 and ∠6 are consecutive interior angles
∠4 and ∠5 are consecutive interior angles
Properties:
They are supplementary
They add up to 180°
Consecutive Interior Angles Proof:
Two-Column Proof
Given: a || b and t with transversal t
Prove: ∠3 and ∠6 are supplementary
| Statement | Reason |
|---|---|
| a || b and t with transversal t | Given |
| ∠2 ≅ ∠6 | Corresponding Angle Postulate |
| m∠2 ≅ m∠6 | Definition of congruent angles |
| ∠3 and ∠2 are supplementary | Linear pair postulate |
| m∠3 + m∠2 = 180° | Definition of supplementary angles |
| m∠3 + m∠6 = 180° | Substitution Property |
| ∠3 and ∠6 are supplementary | Definition of supplementary angles |
Final Answer
They are supplementary
They add up to 180°
They add up to 180°
