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E is a point on the side… (Class 10 Maths Basic 2023, Q28a)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 28(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerTriangles

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ABE CFB.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Look for two pairs of equal angles in the two triangles.

Hint 2

Opposite angles of a parallelogram are equal; also AE ∥ BC with BE as transversal.

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 AD produced beyond D to E; BE drawn cutting CD at F.

    1 mark

  2. In and : [opposite angles of a parallelogram are equal].

    ½ mark

  3. [alternate interior angles, since (AD ∥ BC) and BE is a transversal].

    ½ mark

  4. Therefore [AA similarity criterion].

    1 mark

Answer: ΔABE ~ ΔCFB by AA similarity

Where the marks are

  • Correct figure (1 mark)
  • ∠A = ∠C, opposite angles of parallelogram (½ mark)
  • ∠AEB = ∠CBF, alternate angles (½ mark)
  • Concludes similarity by AA (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 paper2023 board paper, set 430/6/1 (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.