CBSE Class 10 Maths (Basic) 2025 · Paper 430/4/1 · Question 34(b)

Triangles 5 marks Hard

In a

△ A B C

P

and

Q

are points on

A B

and

A C

respectively such that

P Q ∥ B C

. Prove that the median

A D

, drawn from

A

B C

, bisects

P Q

Median through parallel line

Answer

Let

A D

meet

P Q

M

. Since

△ A P M \sim △ A B D

and

△ A M Q \sim △ A D C

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

; as

B D = D C

, we get

P M = M Q

. Hence the median

A D

bisects

P Q

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