Question

triangle ABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD=AB. Show that angle BCD is a right angle.

Answer 1

Answer: angleBCD=90

Step-by-step explanation: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.