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 congruent triangles. By the properties of congruent triangles (corresponding parts of congruent triangles are congruent), the opposite sides of the parallelogram (which are corresponding sides of the congruent triangles) are congruent. Congruent rectangles or similar rectangles are not relevant as we are dealing with a parallelogram. Similar triangles would give proportional sides, not congruent sides.

Answer:

congruent triangles