Skip to content

D is a point on side BC… (Class 10 Maths Basic 2025, Q22)

questionbuddy.in/q/cbse-10-maths-2025-430-2-1-q22-point-side-abc-such-adc

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22

Set in the CBSE Class 10 board exam of 2025, 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 ADC = BAC. Prove that .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 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 contain angle C.

Hint 2

Match the given equal angles carefully: ∠ADC in △ADC corresponds to ∠BAC in △BAC.

Hint 3

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. Figure: with D on BC, and marked equal to .

    ½ mark

  2. In and : [given] and [common angle C].

    ½ mark

  3. [AA similarity criterion].

    ½ mark

  4. Corresponding sides are proportional: . Hence proved.

    ½ mark

Answer: (AA), so , giving .

Where the marks are

  • Correct figure (½ mark)
  • States the two pairs of equal angles with reasons (½ mark)
  • Concludes similarity by AA (½ mark)
  • Writes the proportion and derives the result (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 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.