Question

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

(i) ΔABC ∼ ΔAMP 

(ii) CA/ PA = BC/ MP

Answer 1

(i)  Given: 

Δ ABC and Δ AMP are the two right triangles.

We know that, 

∠AMP = ∠B = 90° 

∠MAP = ∠BAC [Vertically Opposite Angles] 

⇒ ΔABC∼ΔAMP   [AA similarity] 

(ii) Since, ΔABC∼ΔAMP 

\(\frac{CA}{PA} = \frac{BC}{MP}\)  [Corresponding sides are proportional] 

Hence proved.