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Point E lies on the… (Class 10 Maths Basic 2025, Q31)

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MathsCBSE Class 10 · Basic · Board exam 2025, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 31

Set in the CBSE Class 10 board exam of 2025, paper 430/5/1, section C, question 31, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31 · 3 marks · Short answerTriangles

Point E lies on the extended side AD of parallelogram ABCD. BE intersects CD at F. Show that (i) (ii) .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/5/1.

Hints

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

Hint 1

In a parallelogram opposite sides are parallel, so AE ∥ BC. Which alternate angles does transversal EB create?

Hint 2

For (ii), use that opposite angles of a parallelogram are equal, together with one pair of alternate angles.

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: parallelogram ABCD with side AD produced beyond D to a point E; segment BE cuts side CD at F. Since ABCD is a parallelogram, AE ∥ BC and AB ∥ DC.

    ½ mark

  2. (i) In △DFE and △CFB:
    [alternate interior angles, DE ∥ BC, transversal EB]
    [alternate interior angles, DE ∥ BC, transversal DC]

    1 mark

  3. ∴ [AA similarity criterion]

    ½ mark

  4. (ii) In △AEB and △CBF:
    [alternate interior angles, AE ∥ BC]
    [opposite angles of a parallelogram are equal, ]

    ½ mark

  5. ∴ [AA similarity criterion]

    ½ mark

Answer: (i) △DFE ~ △CFB by AA; (ii) △AEB ~ △CBF by AA.

Where the marks are

  • Correct figure (½ mark)
  • Two pairs of equal angles in △DFE and △CFB with reasons (1 mark)
  • Concludes △DFE ~ △CFB by AA (½ mark)
  • Two pairs of equal angles in △AEB and △CBF with reasons (½ mark)
  • Concludes △AEB ~ △CBF by AA (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 430/5/1 (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.