Question

pqr is an isosceles triangle right angled at r prove that PQ² =2pq²

Answer 1

as it's a right angle
apply pythagorus

Also isosceles so height and base are equal

so pq)^2 = pr^2 + pr^2
= 2pr)^2

Answer 2

In triangle pqr

Angle r = 90

side rq = rp (isosceles triangle)

pq is the hypotenuse of the triangle

by pythagoras theorem,

we can say that

pq^2 = rq^2 + rp^2

pq^2 = rq^2 + rq^2 (rp = rq)

therefore pq^2 = 2rq^2

hence proved