Question

In a triangle ABC, AC = AB and the altitude AD bisects BC. Prove that ΔADC ≅ ΔADB.

Answer 1

Given: AC = AB, ∠ADC = ∠ADB = 90° and BD = DC

To Prove: ΔADB ≅ ΔADC

Proof:

In ΔADB and ΔADC:

AB = AC (Given)

AD = AD (Common)

BD = DC (Given)

∴ ΔADB ≅ ΔADC (SSS congruency)