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QR/QS = QT/PR and ∠ 1 = ∠ 2… (Class 10 Maths 2025, Q24b)

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

CBSE Class 10 Mathematics Standard 2025: question 24(b)

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

Q24(b) · 2 marks · Very short answerTriangles

In the given figure, and , show that .

Figure in the paper: Points Q, S, R lie on a horizontal line in that order. P is above, joined to Q, S and R. T is above P, with T joined to Q (line QT passes through P) and to R. Angle 1 is marked at Q (between QR and QP) and angle 2 is marked at R (angle PRS/between RQ and RP). See it in the official paper.

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

Hints

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

Hint 1

Equal angles in tell you something about two of its sides.

Hint 2

Replace PR by PQ in the given ratio, then look for an angle shared by both 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.

  1. In , , i.e. . Therefore [sides opposite equal angles are equal].

    ½ mark

  2. Given . Replacing PR by PQ gives , i.e. .

    ½ mark

  3. In and : (common angle at Q).

    ½ mark

  4. The included angle is equal and the sides containing it are proportional, so [SAS similarity criterion].

    ½ mark

Answer: (SAS similarity)

Where the marks are

  • Deduces PR = PQ from (½ mark)
  • Rewrites the ratio as (½ mark)
  • Identifies the common angle at 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 30/1/1 (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.