Question

triangle ABC is an isosceles triangle such that AB= AC side BA is produced to a point l such that AB=AD prove that angle BCD is a right angle​

Answer 1

Answer:

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In △ABC, we have

AB=AC ∣ given

∠ACB = ∠ABC ... (1) ∣ Since angles opp. to equal sides are equal

Now, AB=AD ∣ Given

∴AD = AC ∣ Since AB = AC

Thus, in △ADC, we have

AD=AC

⇒∠ACD = ∠ADC ... (2) ∣ Since angles opp. to equal sides are equal

Adding (1) and (2) , we get

∠ACB + ∠ACD = ∠ABC + ∠ADC

⇒∠BCD = ∠ABC + ∠BDC ∣ Since∠ADC = ∠BDC

⇒∠BCD+∠BCD=∠ABC+∠BDC+∠BCD ∣ Adding ∠BCD on both sides

⇒2∠BCD=180°

∣ Angle sum property

⇒∠BCD=90°

Hence, ∠BCD is a right angle.