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QR/QS = QT/PR and ∠ 1 =… (Class 10 Maths Basic 2025, Q22b)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, section B, question 22(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(b) · 2 marks · Very short answerTriangles

In the given figure, and . Prove that .

Figure in the paper: Triangle QRT with P on side QT and S on side QR. Segment PR joins P to R, and segment PS joins P to S. Angle 2 is marked at vertex Q (between QS/QR and QP/QT) and angle 1 is marked at vertex R (between RP and RQ). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Equal angles ∠1 and ∠2 sit in triangle PQR. What does that tell you about two of its sides?

Hint 2

Replace PR 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. . Hence [sides opposite equal angles are equal].

    ½ mark

  2. Given . Putting gives , i.e. .

    ½ mark

  3. In and : , since this is , common to both.

    ½ mark

  4. The sides including the equal angle are proportional, so [SAS similarity criterion].

    ½ mark

Answer: ΔPQS ~ ΔTQR by SAS similarity

Where the marks are

  • Uses ∠1 = ∠2 to get PQ = PR (½ mark)
  • Replaces PR by PQ to get (½ mark)
  • Notes ∠Q is common (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 430/3/1 (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.