Class 10 Maths · Triangles · NCERT Exercise 6.3 · Question 12

Triangles Medium

Sides

A B

and

B C

and median

A D

of a triangle

A B C

are respectively proportional to sides

P Q

and

QR

and median

P M

△ P QR

(see Fig. 6.41). Show that

△ A B C \sim △ P QR

Fig. 6.41

Answer

Since

D, M

are midpoints,

\frac{B D}{QM} = \frac{B C}{QR}

, so

△ A B D \sim △ P QM

by SSS similarity, giving

∠ B = ∠ Q

. With

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

and this equal included angle,

△ A B C \sim △ P QR

by the SAS similarity criterion.

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