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The diagonal BD of a… (Class 10 Maths 2025, Q33a)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/1/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 33(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/1/1, section D, question 33(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(a) · 5 marks · Long answerTriangles

The diagonal BD of a parallelogram ABCD intersects the line segment AE at the point F, where E is any point on the side BC. Prove that .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/1/1.

Hints

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

Hint 1

Look for two triangles that have F as a common vertex, one containing DF and FA and the other containing FB and EF.

Hint 2

AD is parallel to BC, and BD is a transversal. Which pairs of angles at F and on BD are then equal?

Hint 3

Show , then write the ratio of their corresponding 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. Figure: Draw parallelogram with at the bottom and at the top. Take a point on side and join . Draw diagonal so that it cuts at .

    1 mark

  2. Since is a parallelogram, , so (because lies on ).

  3. In and :

    • [vertically opposite angles]
    • [alternate interior angles, , transversal ]

    So [AA similarity criterion].

    2 marks

  4. Corresponding sides of similar triangles are proportional:

    1 mark

  5. From , cross-multiply to get . Hence proved.

    1 mark

Answer: (AA), so , i.e. . Proved.

Where the marks are

  • Correct labelled figure of the parallelogram with E on BC, AE and BD meeting at F (1 mark)
  • Proves using vertically opposite angles and alternate angles (AA), with reasons (2 marks)
  • Writes the ratio of corresponding sides (1 mark)
  • Cross-multiplies to reach (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 paper2025 board paper, set 30/1/1 (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.