Question

If D is the mid-point of the side BC in ∆ABC where AB = AC, then ∠ADC is ______.

Options

• 60°

• 45°

• 120°

• 90°

Answer 1

If D is the mid-point of the side BC in ∆ABC where AB = AC, then ∠ADC is 90°.

Explanation:

In ∆ABD and ∆ACD,

AD = AD   ...[Common]

AB = AC  ...[Given]

BD = CD  ...[D is the mid-point of BC]

∴ ∆ABD ≅ ∆ACD  ...[SSS criterion]

∴ ∠ADB = ∆ADC ...[By C.P.C.T]

But ∠ADB + ∠ADC = 180°  ...[∵ BC is a straight line]

⇒ ∠ADC + ∠ADC = 180°

⇒ 2∠ADC = 180°

⇒ ∠ADC = 90°