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ABCD is a quadrilateral… (Class 10 Maths 2024, Q24)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 24

Set in the CBSE Class 10 board exam of 2024, paper 30/1/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24 · 2 marks · Very short answerTriangles

In the given figure, ABCD is a quadrilateral. Diagonal BD bisects and both. Prove that:

  1. (i)

    1 mark
  2. (ii)

    1 mark

Figure in the paper: Quadrilateral ABCD with vertices A (bottom left), B (bottom right), C (top right), D (top left). Diagonal BD is drawn, joining B and D. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/1/1.

Hints

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

Hint 1

What does it mean for BD to bisect ? Write down the two equal angles it gives at B.

Hint 2

Two pairs of equal angles give a similarity criterion. For (ii), notice that BD is a side of both triangles.

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. (i) Name the angles. Since BD bisects , . Since BD bisects , .

  2. (i) In and :

    • [BD bisects ]
    • [BD bisects ]

    [AA similarity criterion].

    1 mark

  3. (ii) From the similarity, corresponding sides are proportional: .

    (Equivalently, the two equal angle pairs and the common side BD give by ASA.)

  4. (ii) Hence . Hence proved.

    1 mark

Answer: (i) by AA; (ii) , since the ratio of sides is (or by ASA congruence).

Where the marks are

  • States the two pairs of equal angles with reasons and concludes by AA (1 mark)
  • Uses the common side BD, through the side ratio or ASA congruence, to conclude (1 mark)

Revise the chapter

  • Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2024 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.