Question

Let ABC be a triangle. Draw a triangle BDC externally on BC such that AB = BD and AC = CD. Prove that ΔABC ≅ ΔDBC.

Answer 1

Given: AB = BD and AC = DC

To Prove: ΔABC ≅ ΔDBC

Proof:

In ΔABC and ΔDBC:

AB = BD (Given)

BC = BC (Common)

AC = DC (Given)

⇒ ΔABC ≅ ΔDBC (SSS congruency)