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Triangle ABC is an isosceles Triangle in which AB=AC. Side BA is produced to D such that AD=AB. Prove that Angle BCD = 90 Degree (answer the question with proper figure and explanations.)

In triangle ABC

AB=AC so,angle ABC=angle ACB

again since AC=AD

Therefore angle ACD=angle ADC

Now let angle ABC=angle ACB=x and
angle ACD =angle ADC=y

so, ABC+BCD+BDC=180

implies x+x+y+y=180

implies 2[x+y]=180

ie, x+y=90

ie, angle BCD=90

Therefore angle BCD is a right angle.


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