Write a two-column proof. Given: 𝐴𝐵̅̅̅̅ || 𝐷𝐸̅̅̅̅ , 𝐴𝐷̅̅̅̅ bisects 𝐵𝐸̅̅̅̅ . Prove: △ABC ≅ △DEC using the ASA postulate

Question

Answer 1

Given: AB is parallel to DE and AD bisects BE.

Prove: Triangle ABC is congruent triangle DEC.

BC is congruent to EC by definition of bisect.

<ABE is congruent to <BED by alternate interior angles.

<ACB is congruent to <ECD by vertical angle theorem.

Triangle ABC is congruent to triangle DEC by ASA congruence theorem (or postulate depending on how the topic is presented).

Answer 2

AC=BD by hypothesis

∠ACB=∠DCE, vertical angles are equal

∠BAC=∠CDE, alternate-interior angles of parallel lines

ΔABC congruent ΔDEC , ASA

BTW: ASA is not a postulate