Question

which of the following are necessary when proving that the opposite angles of a parallelogram are congruent? check all that apply. a. corresponding parts of similar triangles are similar. b. opposite sides are perpendicular. c. corresponding parts of congruent triangles are congruent. d. opposite sides are congruent.

Explanation:

To prove opposite angles of a parallelogram are congruent, a common method involves drawing a diagonal to form two triangles. Using the definition of a parallelogram (opposite sides parallel), alternate interior angles from parallel lines, and a common diagonal, the triangles are proven congruent (ASA). Corresponding parts of congruent triangles (CPCTC) then show opposite angles are congruent. Similar triangles (A) are irrelevant, perpendicular sides (B) are not a property of parallelograms, and opposite sides congruent (D) is a result, not a necessary premise.

Answer:

C. Corresponding parts of congruent triangles are congruent.