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D is a point on the side BC of… (Class 10 Maths 2025, Q24a)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24(a)

Set in the CBSE Class 10 board exam of 2025, paper 30/2/1, section B, question 24(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(a) · 2 marks · Very short answerTriangles

In the given figure, D is a point on the side BC of such that . Show that .

Figure in the paper: Triangle ABC with A at the top, B at bottom-left and C at bottom-right. D lies on side BC between B and C. Segment AD is drawn. The angle at A (BAC) and the angle at D (ADC) are marked. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/2/1.

Hints

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

Hint 1

Look for two triangles that both contain sides CA, CD and CB.

Hint 2

Triangles ACD and BCA share angle C, and one more pair of angles is given equal.

Hint 3

Once they are similar, write the ratio of corresponding sides and cross-multiply.

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. Compare and :

    • [given]
    • [common angle ]

    So [AA similarity criterion].

    1 mark

  2. Corresponding sides of similar triangles are proportional (A↔B, C↔C, D↔A):

    ½ mark

  3. Cross-multiplying gives . Hence proved.

    ½ mark

Answer: (AA), so , which gives

Where the marks are

  • Proves by AA, with the given angle and the common angle (1 mark)
  • Writes the correct ratio of corresponding sides (1/2 mark)
  • Concludes (1/2 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 paper2025 board paper, set 30/2/1 (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.