CBSE Class 10 Maths (Standard) 2024 · Paper 30/5/1 · Question 34(b)

Triangles 5 marks Medium

Sides

A B

and

A C

and median

A D

of a

△ A B C

are respectively proportional to sides

P Q

and

P R

and median

P M

of another

△ P QR

. Show that

△ A B C \sim △ P QR

Answer

Produce

A D

E

and

P M

N

with

D E = A D

M N = P M

. Then

A B E C

and

P QN R

are parallelograms, so

B E = A C

QN = P R

, and

\frac{A B}{P Q} = \frac{B E}{QN} = \frac{A E}{P N}

, giving

△ A B E \sim △ P QN

(SSS). Hence

∠ B A E = ∠ QP N

and, through alternate angles,

∠ E A C = ∠ N P R

, so

∠ B A C = ∠ QP R

. With

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

△ A B C \sim △ P QR

(SAS). Hence proved.

🔒 Step-by-step solution