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. By using properties like alternate interior angles (from the parallel sides of the parallelogram) and the common diagonal, we can show that these two triangles are congruent (using ASA, SAS, etc. congruence criteria). Once the triangles are congruent, their corresponding sides (which are the opposite sides of the parallelogram) are congruent. Concepts of congruent rectangles or similar rectangles/similar triangles are not relevant here as rectangles are a specific type of parallelogram and the proof for general parallelograms uses triangle congruence, not similarity (similarity is about proportional sides, not congruent sides).

Answer:

C. congruent triangles