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Diagonals AC and BD of… (Class 10 Maths 2023, Q25B)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 25(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section B, question 25(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25(B) · 2 marks · Very short answerTriangles

Diagonals AC and BD of trapezium ABCD with AB DC intersect each other at point O. Show that .

Figure in the paper: Trapezium ABCD with AB at the bottom and DC at the top, AB parallel to DC. Diagonals AC and BD intersect at O. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

AB ∥ DC, so look for alternate angles formed by the diagonals.

Hint 2

Prove triangles AOB and COD are similar, then compare 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. In and : [alternate angles, AB ∥ DC, AC transversal] and [alternate angles, BD transversal]. Hence [AA similarity].

    1½ marks

  2. Corresponding sides of similar triangles are proportional, so .

    ½ mark

Answer: (AA), hence .

Where the marks are

  • Shows the two pairs of equal alternate angles and concludes (1½ marks)
  • Writes the ratio of corresponding sides (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 paper2023 board paper, set 30/6/1 (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.