CBSE Class 10 Maths (Standard) 2024 · Paper 30/4/1 · Question 33(b)

Triangles 5 marks Medium

Sides

A B

B C

and the median

A D

△ A B C

are respectively proportional to sides

P Q

QR

and the median

P M

of another

△ P QR

. Prove that

△ A B C \sim △ P QR

Triangles ABC and PQR with medians AD and PM

Answer

△ A B C \sim △ P QR

: from

\frac{A B}{P Q} = \frac{B D}{QM} = \frac{A D}{P M}

we get

△ A B D \sim △ P QM

(SSS), so

∠ B = ∠ Q

; with

\frac{A B}{P Q} = \frac{B C}{QR}

this gives

△ A B C \sim △ P QR

(SAS). Hence proved.

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