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If the diagonals of a… (Class 10 Maths 2024, Q11)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2024: question 11

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQTriangles

If the diagonals of a quadrilateral divide each other proportionally, then it is a:

  1. (A)parallelogram
  2. (B)rectangle
  3. (C)square
  4. (D)trapezium

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Look at the triangles formed by the diagonals.

Hint 2

Proportional parts give similar triangles and hence one pair of parallel sides.

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. If the diagonals AC and BD meet at O with , then (SAS similarity).

  2. So (alternate angles), which gives AB ∥ CD. The quadrilateral is therefore a trapezium, option (D).

    1 mark

Answer: Trapezium, option (D)

Where the marks are

  • Identifies the quadrilateral as a trapezium, option (D) (1 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 paper2024 board paper, set 30/3/1 (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.