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State the SAS criteria of… (Class 10 Maths Basic 2025, Q33)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2025: question 33

Set in the CBSE Class 10 board exam of 2025, paper 430/2/1, section D, question 33, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 5 marks · Long answerTriangles

State the SAS criteria of similarity of two triangles. In the given figure, it is given that . Use the SAS criteria to prove that AD CB.

Figure in the paper: Two line segments AB and CD cross at point O. A is at upper left, B at lower right, C at upper right, D at lower left. O lies between A and B and between C and D. The segments AD and CB are the other two sides. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/2/1.

Hints

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

Hint 1

Rewrite OA·OC = OB·OD as a ratio of sides of two triangles meeting at O.

Hint 2

Which angles at O are equal in triangles OAD and OBC?

Hint 3

From similarity, find two equal alternate angles on transversal AB.

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. SAS similarity criterion: If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, then the two triangles are similar.

    1 mark

  2. Given . To prove . In and : from the given, .

    1 mark

  3. [vertically opposite angles].

    ½ mark

  4. [SAS similarity criterion].

    1 mark

  5. Corresponding angles of similar triangles are equal: , i.e. .

    1 mark

  6. These are alternate interior angles made by transversal AB with lines AD and CB, and they are equal. Hence .

    ½ mark

Answer: △OAD ~ △OBC (SAS), so ∠A = ∠B (alternate angles) ⇒ AD ∥ CB

Where the marks are

  • Correct statement of SAS similarity (1 mark)
  • Writes from the given (1 mark)
  • Vertically opposite angles equal (½ mark)
  • Concludes by SAS (1 mark)
  • Gets (1 mark)
  • Concludes AD ∥ CB using alternate angles (½ mark)

Revise the chapter

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 430/2/1 (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.