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Question

Given: BA≅BC and AE≅CD.

Prove: BE≅BD. B

A E D C

Answer 1

Connect B to A, E, D, and C by line segments and connect A, E, D, and C by a line segment.

Then, we have ΔABC, ΔAEB, and ΔBDC.

Using ΔABC, since BA ≅ BC, ∠BAC ≅ ∠BCA

So, in triangles AEB and BDC, ∠BAE ≅ ∠BCD

Since AE ≅ CD, we have ΔAEB ≅ ΔBCD by side-angle-side (SAS)

So, BE ≅ BD by CPCTC (corresponding parts of congruent triangles are congruent.