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Prove that if a line is drawn… (Class 10 Maths 2026, Q34a)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2026: question 34(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section D, question 34(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(a) · 5 marks · Long answerTriangles

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Join BE and CD, and draw perpendiculars from E to AB and from D to AC.

Hint 2

Compare areas of triangles that share a height; △BDE and △DEC lie between the same parallels.

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. Figure: Triangle ABC with D on AB and E on AC such that DE ∥ BC; BE and CD joined; EM ⟂ AB (M on AB) and DN ⟂ AC (N on AC).
    Given: In △ABC, DE ∥ BC, meeting AB at D and AC at E.
    To prove:
    Construction: Join BE and CD; draw EM ⟂ AB and DN ⟂ AC.

    2 marks

  2. ...(1) [same height EM]

    1 mark

  3. ...(2) [same height DN]

    1 mark

  4. △BDE and △DEC are on the same base DE and between the same parallels DE and BC, so ...(3). From (1), (2), (3): . Hence proved.

    1 mark

Answer: Proved: (Basic Proportionality Theorem)

Where the marks are

  • Correct figure, given, to prove and construction (2 marks)
  • Area ratio of △ADE and △BDE equals AD/DB (1 mark)
  • Area ratio of △ADE and △DEC equals AE/EC (1 mark)
  • Equal areas of △BDE and △DEC with reason, and conclusion (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 paper2026 board paper, set 30/2/1 (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.