MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerTriangles

AD and PS are medians of triangles ABC and PQR respectively such that $△ A B D \sim △ P QS$ . Prove that $△ A B C \sim △ P QR$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

Write down the equal ratios and equal angles that come from $△ A B D \sim △ P QS$ .

Hint 2

A median meets the opposite side at its midpoint, so BD is half of BC.

Hint 3

Two proportional sides with the included angle equal give SAS similarity.

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.

Figure: draw $△ A B C$ with median AD (D the midpoint of BC) and $△ P QR$ with median PS (S the midpoint of QR).
½ mark
Since $△ A B D \sim △ P QS$ , $\frac{A B}{P Q} = \frac{B D}{QS}$ . As $B D = \frac{1}{2} B C$ and $QS = \frac{1}{2} QR$ [D, S are midpoints]: $\frac{A B}{P Q} = \frac{\frac{1}{2} B C}{\frac{1}{2} QR}$
$\Rightarrow \frac{A B}{P Q} = \frac{B C}{QR}$
½ mark
Also $∠ B = ∠ Q$ [corresponding angles of similar triangles ABD and PQS].
½ mark
Hence $△ A B C \sim △ P QR$ [SAS similarity criterion].
½ mark

Answer: $△ A B C \sim △ P QR$ by SAS similarity.

Where the marks are

Draws a correct figure (½ mark)
Deduces $\frac{A B}{P Q} = \frac{B C}{QR}$ using $B D = \frac{B C}{2}$ and $QS = \frac{QR}{2}$ (½ mark)
States $∠ B = ∠ Q$ (½ mark)
Concludes similarity by SAS (½ 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 paper2025 board paper, set 30/5/1 (Standard): 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 Standard 2025: question 24

Hints

Step-by-step solution

Revise the chapter

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