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E is a point on the side CB… (Class 10 Maths 2023, Q28)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 28

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerTriangles

In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with AB = AC. If AD BC and EF AC, then prove that .

Figure in the paper: Isosceles triangle ABC with apex A at top, B and C on the horizontal base with C on the right. AD is drawn from A perpendicular to BC, with D on BC (right angle marked). E lies on line CB extended beyond B to the left. EF is drawn from E to F on side AC, with right angle marked at F. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

What does AB = AC tell you about angles B and C?

Hint 2

Both triangles have a right angle. Find one more pair of equal angles.

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 , AB = AC, so [angles opposite equal sides].

    1 mark

  2. In and : [AD ⟂ BC, EF ⟂ AC] and [from the first step, since is the same angle as ].

    1 mark

  3. Therefore [AA similarity criterion].

    1 mark

Answer: by AA similarity.

Where the marks are

  • Uses AB = AC to get (1 mark)
  • Identifies the pair of right angles and the pair of equal base angles (1 mark)
  • Concludes similarity by AA (1 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 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.