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P is a point on the side BC of… (Class 10 Maths 2025, Q24)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2025: question 24

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, 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

P is a point on the side BC of such that . Prove that .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Look for two triangles that both contain side AC and angle C.

Hint 2

Compare and : one angle is given equal, angle C is common.

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: with P on BC, AP joined; and marked equal.

    ½ mark

  2. In and : (given) and (common). So [AA similarity].

    1 mark

  3. Corresponding sides are proportional: . Hence proved.

    ½ mark

Answer: (proved)

Where the marks are

  • Correct figure (½ mark)
  • Proves by AA (1 mark)
  • Writes proportion and concludes (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 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.