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