Question

question 5 of 10

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. segment addition postulate.
c. angle addition postulate.
d. corresponding parts of congruent triangles are congruent.

Explanation:

Analyze the proof requirements

Using the Parallelogram Proofs knowledge point
To prove that the opposite angles of a parallelogram are congruent, we draw a diagonal to divide the parallelogram into two triangles. We then prove these triangles are congruent using triangle congruence postulates (such as ASA or SSS).

Apply triangle congruence consequences

Using the CPCTC Application knowledge point
Once the triangles are proven congruent, we establish that their corresponding parts are congruent. This directly uses the principle that corresponding parts of congruent triangles are congruent (CPCTC) to show that one pair of opposite angles is congruent.

Combine split angles

To prove the other pair of opposite angles (which are split by the diagonal) are congruent, we add the adjacent congruent angle parts together. This step requires the Angle Addition Postulate to combine the smaller angles into the full opposite angles of the parallelogram.

Answer:

• (A) Corresponding parts of similar triangles are similar.

<mcq-option>(B) Segment Addition Postulate.</mcq-correct>

• (C) Angle Addition Postulate. (Correct answer)
• (D) Corresponding parts of congruent triangles are congruent. (Correct answer)