Please answer as soon as possible! Given: ABCD is a parallelogram.

Prove: ∠A ≅ ∠C and ∠B ≅ ∠D

Parallelogram A B C D is shown.

By the definition of a ▱, AD∥BC and AB∥DC.

Using, AD as a transversal, ∠A and ∠
D
are same-side interior angles, so they are
supplementary
. Using side
CD
as a transversal, ∠B and ∠C are same-side interior angles, so they are supplementary. Using AB as a transversal, ∠A and ∠B are same-side interior angles, so they are supplementary.

Therefore, ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠
.