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ABC and AMP are two right… (Class 10 Maths Basic 2023, Q25)

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MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2023: question 25

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerTriangles

In the given figure, ABC and AMP are two right triangles, right angled at B and M, respectively. Prove that .

Figure in the paper: Triangle ABC with a right angle at B, where B lies on the base line AP. Point M lies on side AC and angle at M is a right angle, with segment MP drawn from M to P on the base line. Points in order on the base: A, B, P. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/1/1.

Hints

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

Hint 1

Look for two pairs of equal angles.

Hint 2

Both triangles share vertex A and each has a right angle.

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].

    ½ mark

  2. [common angle at A].

    1 mark

  3. Therefore [AA similarity criterion].

    ½ mark

Answer: by AA similarity

Where the marks are

  • Right angles at B and M equal (½ mark)
  • Common angle A (1 mark)
  • Concludes similarity by AA (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 paper2023 board paper, set 430/1/1 (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.