Skip to content

Sides AB and BC and median AD… (Class 10 Maths 2023, Q35a)

questionbuddy.in/q/cbse-10-maths-2023-30-2-1-q35a-sides-median-triangle-abc-respectively

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/2/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2023: question 35(a)

Set in the CBSE Class 10 board exam of 2023, paper 30/2/1, section D, question 35(a), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q35(a) · 5 marks · Long answerTriangles

Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of . Show that .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/2/1.

Hints

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

Hint 1

A median cuts the opposite side into two equal halves. How can you write BC and QR using BD and QM?

Hint 2

Look for a pair of smaller triangles, one inside each figure, whose three sides are all in the same ratio.

Hint 3

Once you get one pair of equal angles from those smaller triangles, use it as the included angle between AB and BC.

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: Draw with median AD (D is the mid-point of BC) and with median PM (M is the mid-point of QR).

    Given: . To prove: .

    1 mark

  2. D and M are mid-points, so and . Substituting in the given ratios:
    , which gives .

    1 mark

  3. All three pairs of corresponding sides of and are in the same ratio, so [SSS similarity criterion].

    1 mark

  4. Corresponding angles of similar triangles are equal, so ...(i)

    ½ mark

  5. Now compare and : (given) and the included angles satisfy [from (i)].

    ½ mark

  6. Therefore [SAS similarity criterion]. Hence proved.

    1 mark

Answer: (SSS) gives ; then (SAS).

Where the marks are

  • Correct labelled figure of both triangles with their medians (1 mark)
  • Uses , to get (1 mark)
  • Concludes by SSS (1 mark)
  • Deduces (½ mark)
  • States the SAS conditions in and (½ mark)
  • Concludes (1 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 paper2023 board paper, set 30/2/1 (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.