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 draw a diagonal of the parallelogram. This divides the parallelogram into two triangles. Then, using the properties of parallelograms (opposite sides are parallel), we can show that these two triangles are congruent (by ASA - Angle - Side - Angle congruence criterion as alternate interior angles are equal due to parallel sides and the diagonal is a common side). Once 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 as we are dealing with parallelograms. Similar triangles would give proportional sides, not congruent sides.

Answer:

congruent triangles