Question

PQ is perpendicular to BA and BD is perpendicular to AP.PQ and BD intersect at R. Prove that ΔABD ∼ ΔAPQ and `"AB"/"AP" = "BD"/"PQ"`.

Answer 1

In ΔABD and ΔAPQ,
∠BDA  ∠PQA = 90°
∠A = ∠A
Therefore, ΔABD ∼ ΔAPQ   ...(AA axiom)

And hence, `"AB"/"AP" = "BD"/"PQ"`.