Please answer as soon as possible!
Given: ABCD is a parallelogram.
Prove: ∠A ≅ ∠C and ∠...
Mathematics, 18.03.2021 01:20 jr928718
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 ∠
.
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