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) CA/PA = BC/MP

Answer 1

SOLUTION :

(i)  Given Δ ABC and Δ AMP are the two right angled triangle & ∠MAP = ∠BAC .

In ∆ ABC and Δ AMP,

∠AMP  = ∠B (each 90°)

∠MAP = ∠BAC (given)

ΔABC∼ΔAMP    (By AA similarity)

(ii) ΔABC ∼ ΔAMP (proved above in part (i)  

So,  CA/PA = BC/MP

[Since, triangles  are Similar ,hence, corresponding Sides will be proportional]

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