Question

In isosceles triangle ABC, AB = AC. The side BA is produced to D such that BA = AD.
Prove that: ∠BCD = 90°

Answer 1

Const: Join CD.

In ΔABC,

AB = AC       ...[ Given ]

∴  ∠C = ∠B .......(i) [angles opp. to equal sides are equal]

In ΔACD,

AC = AD     ...[Given]

∴  ∠ADC = ∠ACD     ...(ii)

Adding (i) and (ii)

∠B + ∠ADC = ∠C + ACD

∠B + ∠ADC = ∠BCD      ...(iii)

In ΔBCD,

∠B + ∠ADC + ∠BCD = 180°

∠BCD + ∠BCD = 180°    ...[From (iii)]

2∠BCD = 180°

∠BCD = 90°