Question

If triangle ABC,right angle B which is 90 degree,AB=BC, BC is produced to a point D . Prove that AD2= 2BC.BD+CD2

Answer 1

Step-by-step explanation:

To prove: AD²= {2BC× BD} + CD²

Given: AB=BC = X (suppose)

Solution:

In triangle ABD we have :

AB²+BD²= AD²

=] x² + {x+CD} ²= AD²

=] x²+x²+CD²+{2CD×BC} = AD²

=] 2BC + CD²+ 2CD.BD= AD²

Thus, Proved!