Skip to content

LM ∥ CB and LN ∥ CD… (Class 10 Maths Basic 2024, Q23b)

questionbuddy.in/q/cbse-10-maths-2024-430-4-1-q23b

MathsCBSE Class 10 · Basic · Board exam 2024, set 430/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2024: question 23(b)

Set in the CBSE Class 10 board exam of 2024, paper 430/4/1, section B, question 23(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(b) · 2 marks · Very short answerTriangles

In the given figure, and . Prove that .

Figure in the paper: Quadrilateral ABCD with diagonal AC. Point L lies on AC. M lies on side AB and N lies on side AD. LM is drawn parallel to CB and LN parallel to CD (arrow marks). See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/4/1.

Hints

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

Hint 1

Diagonal AC splits the figure into two triangles, each containing one of the parallel lines.

Hint 2

Apply the Basic Proportionality Theorem in △ABC and in △ADC. Both give a ratio involving AL/AC.

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 , , so by the Basic Proportionality Theorem, ...(i)

    0.75 marks

  2. In , , so by BPT, ...(ii)

    0.75 marks

  3. From (i) and (ii), . Hence proved.

    ½ mark

Answer: AM/AB = AL/AC = AN/AD, hence AM/AB = AN/AD.

Where the marks are

  • Applies BPT in △ABC to get AM/AB = AL/AC, and in △ADC to get AN/AD = AL/AC (1½ marks)
  • Equates the two ratios to conclude AM/AB = AN/AD (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 paper2024 board paper, set 430/4/1 (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.