Question

In triangle ABC, AP is perpendicular TO BC. AB=a units, AC=b units , BP=c units, PC=d units. Prove that (a + b) (a - b) = (c + d) (c - d)

Answer 1

$a^2=h^2+c^2\dots \dots \left(i\right)$
$b^2=h^2+d^2\dots \dots \left(ii\right)$
Pythagoras theorem

(i) - (ii)
$a^2-b^2=c^2-d^2$
$(a-b)(a+b)=(c-d)(1+d)$
Hence Proved.