CBSE Class 10 Maths (Basic) 2026 · Paper 430/3/1 · Question 23(b)

Triangles 2 marks Medium

In the given figure,

△ P QR

is a right triangle, right-angled at

Q

and

QS ⊥ P R

. Prove that

△ P QS \sim △ QR S

Part (b) : △PQR right-angled at Q with QS ⊥ PR

Answer

△ P QS

and

△ QR S

∠ P S Q = ∠ QS R = 9 0^{\circ}

and

∠ QP S = ∠ S QR

(each is complementary to

∠ P QS

), so by the AA similarity criterion

△ P QS \sim △ QR S

. Hence proved in either alternative.

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