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. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Opposite sides are congruent.
SUBMIT

Answer 1

B. CPCTC

D. opposite sides are congruent

Explanation:

You want to know the necessary claims for proving opposite angles are congruent in a parallelogram.

Proof

Given parallelogram ABCD and diagonal AC, you can prove opposite angles congruent in this way:

AB≅CD and BC≅DA . . . . . opposite sides are congruent

AC≅CA . . . . . . . . . . . . . . reflexive property of congruence

∆ABC≅∆CDA . . . . . . . . . . . SSS congruence

∠B ≅ ∠D . . . . . . . . . . . . Corresponding parts of congruent triangles

When doing the proof, the necessary claims are ...

B. Corresponding parts of congruent triangles are congruent

D. Opposite sides are congruent.

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