Question

If a transversal intersects two parallel lines, prove the following:

a) It's corresponding angle pairs are equal.
b) Each pair of its interior angles on the same side are supplementary.

A. True
B. False

Answer 1

The statement is true; corresponding angle pairs are equal and each pair of interior angles on the same side of the transversal are supplementary when a transversal intersects two parallel lines.

Step-by-step explanation:

When a transversal intersects two parallel lines, several angle relationships are formed. Firstly, corresponding angles created are equal, and this can be proven using the fact that each pair of corresponding angles are on the same side of the transversal and similarly positioned at each intersection. Secondly, each pair of interior angles on the same side of the transversal are supplementary, meaning that their measures add up to 180 degrees. This is because the lines are parallel and the alternate interior angles are equal, leading to the conclusion that when these angles are added to their adjacent corresponding angles (which are congruent), they sum to 180 degrees.

To prove these statements:

1. Identify a pair of corresponding angles and note that they are equal in measure because they are congruent due to the parallel lines. This proves part a) of the question.
2. Identify a pair of consecutive interior angles on the same side of the transversal. Since one angle is supplementary to the corresponding angle (which is equal to the alternate interior angle), the two consecutive interior angles must sum to 180 degrees, proving part b) of the question.

Therefore, both statements a) and b) are True.