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Home » 10. 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
10. 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
CBSE | Class 10 | Exercise 4.5 | Maths | RD Sharma | Triangles
10. 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

Solution:

(i)  Given:

Δ ABC and Δ AMP are the two right triangles.

To prove :

ΔABC ∼ ΔAMP

Proof :

∠AMP = ∠B = 90o

∠MAP = ∠BAC (Vertically Opposite Angles)

⇒ ΔABC∼ΔAMP     (AA similarity)

(ii)  ΔABC∼ΔAMP

CA/ PA = BC/ MP (Corresponding sides are proportional)

Hence proved.

i

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