MathsCBSE Class 10 · Standard · Board exam 2025, set 30/3/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 34(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/3/1, section D, question 34(b), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(b) · 5 marks · Long answerTriangles

Sides AB and BC and median AD of triangle ABC are respectively proportional to sides PQ and QR and median PM of $Δ$ PQR. Show that $Δ$ ABC $\sim$ $Δ$ PQR.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/3/1.

Hints

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

Hint 1

A median bisects the opposite side, so BD is half of BC and QM is half of QR.

Hint 2

First show $△ A B D \sim △ P QM$ by SSS to get $∠ B = ∠ Q$ , then apply SAS to the whole triangles.

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 is the mid-point of BC), and $△ P QR$ with median PM (M is the mid-point of QR).
Given: $\frac{A B}{P Q} = \frac{B C}{QR} = \frac{A D}{P M}$ . To prove: $△ A B C \sim △ P QR$ .
1 mark
Since D and M are mid-points, $B C = 2 B D$ and $QR = 2 QM$ . So
$\frac{A B}{P Q} = \frac{2 B D}{2 QM} = \frac{A D}{P M} \Rightarrow \frac{A B}{P Q} = \frac{B D}{QM} = \frac{A D}{P M}$
1 mark
Therefore $△ A B D \sim △ P QM$ [SSS similarity].
1 mark
So $∠ B = ∠ Q$ [corresponding angles of similar triangles].
½ mark
In $△ A B C$ and $△ P QR$ : $\frac{A B}{P Q} = \frac{B C}{QR}$ (given) and the included angles are equal, $∠ B = ∠ Q$ .
1 mark
Hence $△ A B C \sim △ P QR$ [SAS similarity].
½ mark

Answer: $△ A B C \sim △ P QR$ (proved using SSS, then SAS similarity)

Where the marks are

Correct labelled figure with both medians (1 mark)
Uses $B C = 2 B D$ , $QR = 2 QM$ to get $\frac{A B}{P Q} = \frac{B D}{QM} = \frac{A D}{P M}$ (1 mark)
$△ A B D \sim △ P QM$ by SSS (1 mark)
Deduces $∠ B = ∠ Q$ (½ mark)
States $\frac{A B}{P Q} = \frac{B C}{QR}$ with included $∠ B = ∠ Q$ (1 mark)
Concludes $△ A B C \sim △ P QR$ 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 30/3/1 (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 34(b)

Hints

Step-by-step solution

Revise the chapter

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