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Assertion (A): ABCD is a… (Class 10 Maths 2024, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedTriangles

Assertion (A): ABCD is a trapezium with DC AB. E and F are points on AD and BC respectively, such that EF AB. Then .

Reason (R): Any line parallel to parallel sides of a trapezium divides the non-parallel sides proportionally.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

Join diagonal AC and use BPT twice.

Hint 2

Is the assertion just a special case of the reason?

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. R is a standard result (join AC; apply BPT in △ADC and △ABC), hence true.

  2. A follows directly from R with EF ∥ AB ∥ DC, so both true and R explains A: option (A).

    1 mark

Answer: Option (A)

Where the marks are

  • Recognises both true and R explains A (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 30/5/1 (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.