CBSE Class 10 Maths (Standard) 2024 · Paper 30/2/1 · Question 33(b)

Triangles 5 marks Medium

Sides

A B

and

A C

and median

A D

△ A B C

are respectively proportional to sides

P Q

and

P R

and median

P M

of another triangle

P QR

. Show that

△ A B C \sim △ P QR

Answer

△ A B C \sim △ P QR

. Hence proved: doubling the medians gives parallelograms

A B E C

and

P QN R

; SSS similarity of

△ A B E, △ P QN

and of

△ A C E, △ P R N

gives

∠ B A C = ∠ QP R

, and SAS similarity with

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

completes the proof.

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