Question

Given: a ll b, <1 = <4

Prove: <2 = <3
Steps
1. a ll b, <1 = <4
2. <1 = <2
3. <2= <4
4. <4= <3
5.<2= <3
What is the reason for Step 4?
A) Given
B Alternate Interior Angle Theorem
Alternate Exterior Angle Theorem
Transitive Property of Congruence

Answer 1

Step 4 in the given proof is justified by the Alternate Exterior Angle Theorem.

The Alternate Exterior Angle Theorem states that when two parallel lines are cut by a transversal, the alternate exterior angles are congruent. In the given problem, a ll b and <1 = <4 are given. By definition, <2 and <3 are alternate exterior angles formed by a transversal intersecting two parallel lines a and b. Therefore, <2 and <3 are congruent by the Alternate Exterior Angle Theorem, which justifies Step 4 in the given proof

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