Triangle ABC is an isosceles triangle with AB=AC, side BA is produced to D such that AB=AD. Prove that angle BCD is a right angle.

In triangle ABC

AB=AC so,angle ABC=angleACB

again since AC=AD

Therefore angleACD=angleADC

Now let angleABC=angleACB=x and angleACD=angleADC=y

so, ABC+BCD+BDC=180

>x+x+y+y=180

>2[x+y]=180

>x+y=90

>BCD=90

Therefore angle BCD is a right angle