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प्रश्न
If D is the mid-point of the side BC in ∆ABC where AB = AC, then ∠ADC is ______.
पर्याय
60°
45°
120s°
90°
उत्तर
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°
APPEARS IN
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