Answer :

Corresponding angles formed when a transversal cuts parallel lines are congruent, and this also applies to alternate interior and exterior-interior angles, proving the parallels.

When parallel lines are cut by a transversal, the corresponding angles are congruent, meaning they have the same measure. This concept is based on the properties of parallel lines and can be understood through geometric proofs. For instance, THEOREM 19 states that if two parallel lines are cut by a third straight line, the alternate-interior angles and also the exterior-interior angles are congruent. Similarly, triangles formed by these intersecting lines and parallel lines can be shown to be similar due to the congruence of corresponding angles, which is further supported by THEOREM 10 that mentions congruent angles created by a transversal cutting parallel lines.

Moreover, it's important to note that congruence of alternate interior angles, which are a specific type of corresponding angles, also serves as evidence of the parallel nature of the lines, according to the corollary in geometry.

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Rewritten by : Barada

Answer:

congruent

Step-by-step explanation:

Given parallel lines cut by transversal, corresponding angles are congruent.