AD and PS are respectively, the medians of △ ABC and △ PQR. If △ ABC ~ △ PQR, then prove that (i) △ ADC ~ △ PSR (ii) AD/PS = BC/QR

(i) △ ADC~△ PSR by SAS; (ii) AD/PS=BC/QR

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2026: question 33(b)

Set in the CBSE Class 10 board exam of 2026, paper 430/4/1, section D, question 33(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(b) · 5 marks · Long answerTriangles

$A D$ and $P S$ are respectively, the medians of $△ A B C$ and $△ P QR$ . If $△ A B C \sim △ P QR$ , then prove that

(i)
$△ A D C \sim △ P S R$
0 marks
(ii)
$\frac{A D}{P S} = \frac{B C}{QR}$
0 marks

Figure in the paper: Two triangles side by side: triangle ABC with median AD (D on BC, B left, C right, A apex); triangle PQR with median PS (S on QR, Q left, R right, P apex). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Write down what $△ A B C \sim △ P QR$ tells you about sides and angles.

Hint 2

A median meets the opposite side at its mid-point, so $D C = \frac{B C}{2}$ and $S R = \frac{QR}{2}$ .

Hint 3

For (ii), use the similarity proved in (i) to compare AD and PS.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) Since $△ A B C \sim △ P QR$ , corresponding sides are proportional: $\frac{A B}{P Q} = \frac{A C}{P R} = \frac{B C}{QR}$ . As D and S are mid-points of BC and QR, $B C = 2 D C$ and $QR = 2 S R$ , so $\frac{B C}{QR} = \frac{2 D C}{2 S R} = \frac{D C}{S R}$ .
2 marks
Hence $\frac{A C}{P R} = \frac{D C}{S R}$ .
½ mark
Also $∠ C = ∠ R$ (corresponding angles of similar triangles). So in $△ A D C$ and $△ P S R$ , two sides are proportional and the included angle is equal; $∴ △ A D C \sim △ P S R$ [SAS similarity].
½ mark
(ii) Since $△ A D C \sim △ P S R$ , $\frac{A D}{P S} = \frac{D C}{S R}$ .
1 mark
$\frac{A D}{P S} = \frac{B C /2}{QR /2} = \frac{B C}{QR}$ . Hence proved.
1 mark

Answer: (i) $△ A D C \sim △ P S R$ by SAS; (ii) $\frac{A D}{P S} = \frac{B C}{QR}$

Where the marks are

Writes ratio of sides from similarity and $\frac{B C}{QR} = \frac{2 D C}{2 S R}$ (2 marks)
Gets $\frac{A C}{P R} = \frac{D C}{S R}$ (½ mark)
Uses $∠ C = ∠ R$ and SAS similarity (½ mark)
Writes $\frac{A D}{P S} = \frac{D C}{S R}$ (1 mark)
Replaces DC, SR by halves of BC, QR to conclude (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/4/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 33(b)

Hints

Step-by-step solution

Revise the chapter

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