In the given figure, DE ∥ AC and DF ∥ AE. Prove that BF/FE = BE/EC.

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/1/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2023: question 31(a)

Set in the CBSE Class 10 board exam of 2023, paper 430/1/1, section C, question 31(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q31(a) · 3 marks · Short answerTriangles

In the given figure, $D E ∥ A C$ and $D F ∥ A E$ . Prove that $\frac{B F}{F E} = \frac{B E}{E C}$ .

Figure in the paper: Triangle ABC with D on side AB and E, F, C on base BC in the order B, F, E, C. A is the apex. DE is drawn parallel to AC and DF is drawn parallel to AE, with F on BC between B and E. 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

Use the Basic Proportionality Theorem in two different triangles.

Hint 2

Both triangles ABE and ABC give a ratio involving $\frac{B D}{D A}$ .

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.

In $△ A B E$ , $D F ∥ A E$ [given], so by the Basic Proportionality Theorem, $\frac{B D}{D A} = \frac{B F}{F E}$ … (i)
1½ marks
In $△ A B C$ , $D E ∥ A C$ [given], so by BPT, $\frac{B D}{D A} = \frac{B E}{E C}$ … (ii)
1 mark
From (i) and (ii), $\frac{B F}{F E} = \frac{B E}{E C}$ . Hence proved.
½ mark

Answer: BF/FE = BE/EC (proved using BPT twice)

Where the marks are

Applies BPT in $△ A B E$ to get (i) (1½ marks)
Applies BPT in $△ A B C$ to get (ii) (1 mark)
Equates the two to conclude (½ 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 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.

CBSE Class 10 Mathematics Basic 2023: question 31(a)

Hints

Step-by-step solution

Revise the chapter

More questions from Triangles