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If PQ ∥ RS, then prove… (Class 10 Maths Basic 2025, Q22a)

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

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

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

Q22(a) · 2 marks · Very short answerTriangles

In the given figure, if , then prove that .

Figure in the paper: Lines PQ and RS are parallel (arrows marked). Segments PS and QR (or RQ) cross at point O, which lies between P and S and between Q and R. P is at top-left, Q below P, R at top-right, S at bottom-right. See it in the official paper.

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

Hints

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

Hint 1

Parallel lines cut by a transversal give equal alternate angles.

Hint 2

PS and QR both act as transversals. You could also use the vertically opposite angles at O.

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 and : and PS is a transversal, so [alternate interior angles].

    1 mark

  2. QR is also a transversal, so [alternate interior angles]. Therefore [AA similarity criterion].

    1 mark

Answer: △POQ ~ △SOR by AA similarity

Where the marks are

  • States one pair of equal alternate angles with the reason (1 mark)
  • States the second pair of equal angles and concludes similarity by AA (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 paper2025 board paper, set 430/1/1 (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.