Question

Give the missing reasons in this proof of the Alternate Interior Angles Theorem.

Given:

Prove:

Answer 1

1. When a transversal intersects two lines, two angles on the same side of the transversal and both on the same relative side of the two lines are called corresponding angles. If the lines are parallel, corresponding angles are congruent. For example, angles 1 and 5 are corresponding, and bec the lines are parallel, they are congruent.

2. Angles such as 1 and 3 are vertical angles. Vertical angles are congruent.

3. Also, let's say <A is congr to <B, and <B is congr to <C, then <A is congr to <C by transitive property of congruence.

These three points I made are hints as to what you need to do to get the reasons you need.