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If PQ ∥ RS, then prove… (Class 10 Maths Basic 2026, Q22a)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22(a)

Set in the CBSE Class 10 board exam of 2026, 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 (arrow marks). Segments PS and QR cross at O; P and Q are on one side, R and S on the other, with P-O-S and Q-O-R. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/1/1.

Hints

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

Hint 1

Look for pairs of equal angles created by the parallel lines.

Hint 2

PS is a transversal of the parallel lines PQ and RS. What do you know about alternate angles?

Hint 3

Two pairs of equal angles are enough. Which similarity criterion is that?

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 is a transversal, so [alternate interior angles].

    1 mark

  2. [vertically opposite angles]. (Also , alternate angles with transversal .)

    ½ mark

  3. Hence [AA similarity criterion].

    ½ mark

Answer: by AA similarity

Where the marks are

  • Uses alternate interior angles (1 mark)
  • Uses vertically opposite angles (½ mark)
  • Concludes similarity by AA criterion (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 paper2026 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.