CBSE Class 10 Maths (Basic) 2025 · Paper 430/3/1 · Question 33(b)

Triangles 5 marks Medium

In the given figure,

C M

and

R N

are respectively, the medians of

△ A B C

and

△ P QR

. If

△ A B C \sim △ P QR

, prove that:

Answer

(i)

△ A M C \sim △ P N R

by SAS similarity, since

\frac{A M}{P N} = \frac{A C}{P R}

and

∠ A = ∠ P

; (ii)

∠ B C M = ∠ A C B - ∠ A C M = ∠ P R Q - ∠ P R N = ∠ QR N

; (iii)

△ B M C \sim △ QN R

by SAS similarity, since

\frac{B M}{QN} = \frac{B C}{QR}

and

∠ B = ∠ Q

. Hence proved.

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