Given that line 𝐴𝐶 and line 𝐷𝐵 intersect at E, with A–E–C and D–E–B, such that AD=BC and line 𝐴𝐷 // line 𝐵𝐶. Prove that line 𝐴𝐶 and line 𝐷𝐵 bisect each other at E.

Answer 1

Triangle AED is congruent to triangle BEC by ASA.

The conclusion follows because corresponding parts of congruent triangles are equal.