Question

Prove that a ΔABC is an isosceles triangle if the altitude AD from A on BC bisects BC.

Answer 1

Given: BD = DC and ∠ADB = ∠ADC = 90°

To Prove: AB = AC

Proof:

In ΔADC and ΔADB:
AD = AD (Common)
BD = DC (Given)

∠ADB = ∠ADC (Given)

ΔADC ≅ ΔADB (SAS congruency)

∴ AB = AC (Corresponding parts of congruent triangles)

Thus, the given triangle is isosceles.