Question

which concept is used to prove that the opposite sides of a parallelogram are congruent?
congruent rectangles
similar rectangles
congruent triangles
similar triangles

Explanation:

To prove that the opposite sides of a parallelogram are congruent, we can draw a diagonal of the parallelogram, which divides it into two triangles. These two triangles are congruent (by SAS congruence criterion, as alternate interior angles are equal and the diagonal is common, and opposite sides are parallel so alternate interior angles are congruent). Once we prove the triangles are congruent, their corresponding sides (which are the opposite sides of the parallelogram) are congruent. Congruent rectangles or similar rectangles are not relevant here as we are dealing with triangles formed in the parallelogram, and similar triangles don't give the congruence of sides directly as needed here.

Answer:

C. congruent triangles