MathsCBSE Class 10 · Standard · Board exam 2025, set 30/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2025: question 33(B)

Set in the CBSE Class 10 board exam of 2025, paper 30/4/1, section D, question 33(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(B) · 5 marks · Long answerTriangles

State basic proportionality theorem. Use it to prove the following : If three parallel lines $l$ , $m$ , $n$ are intersected by transversals $q$ and $s$ as shown in the adjoining figure, then $\frac{A B}{B C} = \frac{D E}{E F}$ .

Figure in the paper: Three parallel horizontal lines l (top), m (middle), n (bottom). Transversal q meets l at A, m at B, n at C. Transversal s meets l at D, m at E, n at F. Arrows mark the lines as parallel. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/4/1.

Hints

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

Hint 1

You need triangles to apply BPT; draw a line joining A to F.

Hint 2

Line $m$ cuts AF at G; apply BPT in $Δ A C F$ and in $Δ A F D$ and compare the common ratio AG/GF.

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.

Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
1 mark
Construction: Join AF; let it cut line $m$ at G.
1 mark
In $Δ A C F$ , $B G ∥ C F$ (parts of $m ∥ n$ ). By BPT: $\frac{A B}{B C} = \frac{A G}{GF}$ ...(i)
1 mark
In $Δ F D A$ , $GE ∥ A D$ (parts of $m ∥ l$ ). By BPT: $\frac{F E}{E D} = \frac{F G}{G A}$ , i.e. $\frac{D E}{E F} = \frac{A G}{GF}$ ...(ii)
1 mark
From (i) and (ii): $\frac{A B}{B C} = \frac{D E}{E F}$ . Hence proved.
1 mark

Answer: BPT stated; $\frac{A B}{B C} = \frac{D E}{E F}$ proved using diagonal AF

Where the marks are

Correct statement of BPT (1 mark)
Construction: join AF meeting m at G (1 mark)
BPT in $Δ A C F$ : $\frac{A B}{B C} = \frac{A G}{GF}$ (1 mark)
BPT in $Δ F D A$ : $\frac{D E}{E F} = \frac{A G}{GF}$ (1 mark)
Combines to conclude (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

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 30/4/1 (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.

CBSE Class 10 Mathematics Standard 2025: question 33(B)

Hints

Step-by-step solution

Revise the chapter

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