Question

If ∆ABC and ∆AMP are two right triangles, right angled at B and M respectively such that ∠MAP = ∠BAC. Prove that

(i) ∆ABC ∼ ∆AMP
(ii) $\frac{\mathrm{CA}}{\mathrm{PA}}=\frac{\mathrm{BC}}{\mathrm{MP}}$

Answer 1

(1) It is given that and are two right angle triangles.

Now, in and , we have

(Given)

(AA Similarity)

(2)

So, (Corresponding sides are proportional)