Question

In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.

Prove that: BD = CD

Answer 1

In ΔADB and ΔADC,

∠ADB = ∠ADC           ...(Since AD is perpendicular to BC)

AB = AC                     ...(given)

AD = AD                    ...(common side)

∴ ΔADB ≅ ΔADC      ...(RHS congruence criterion)

⇒ BD = CD               ...(cpct)