Question

∆ABC is an isosceles triangle in which AB = AC .

Side BA is produced to D such that AD =AB .

Show that BCD is a right angle.​

Answer 1

Given: ΔABC is an isosceles triangle

           AB = AC

           AD = AB

To Prove: ∠BCD = 90°

Proof: In ΔABC,

AB = AC

⇒ ∠ACB = ∠ABC →(1)  (∠s opp. to equal sides)

In ΔACD,

AC = AD

⇒ ∠ADC = ∠ACD →(2) (∠s opp. to equal sides)

In ΔBCD,

∠ABC + ∠BCD + ∠BDC = 180° (angle sum property)

⇒ ∠ACB + ∠BCD + ∠ACD = 180° (from (1) & (2))

⇒ (∠ACB + ∠ACD) + ∠BCD = 180°

⇒ (∠BCD) + ∠BCD = 180°

⇒ 2∠BCD = 180°

⇒ ∠BCD = 90°

Hence, proved