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D is a point on side BC… (Class 10 Maths Basic 2026, Q22)

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MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2026: question 22

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerTriangles

D is a point on side BC of ABC such that . Prove that .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

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

Hint 1

Look for two triangles that both have the angle at C.

Hint 2

Compare with : which pairs of angles are equal?

Hint 3

Once the triangles are similar, write the side ratio that contains CA, CB and CD.

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 : [given] and [common angle ].

    1 mark

  2. [AA similarity]. Corresponding sides are proportional, so .

    ½ mark

  3. Cross-multiplying gives . Hence proved.

    ½ mark

Answer: (AA), so , giving .

Where the marks are

  • Shows that the two pairs of angles are equal, giving reasons (1 mark)
  • States and writes the ratio of corresponding sides (½ mark)
  • Concludes (½ 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 paper2026 board paper, set 430/2/1 (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.