Question

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

Options

• 60°

• 45°

• 120s°

• 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°