In the given figure, AB ∥ DE and AC ∥ DF. Show that △ ABC ~ △ DEF. If BC = 10 cm, EB = CF = 5 cm and AB = 7 cm, then find the length DE.

△ ABC~△ DEF (AA); DE = 14 cm

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 23

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section B, question 23, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23 · 2 marks · Very short answerTriangles

In the given figure, AB $∥$ DE and AC $∥$ DF. Show that $△ A B C \sim △ D E F$ . If BC = 10 cm, EB = CF = 5 cm and AB = 7 cm, then find the length DE.

Figure in the paper: Triangle DEF with D at top, E at bottom left, F at bottom right. Points B and C lie on segment EF in that order (E, B, C, F), and A lies inside the triangle, joined to B and C. Segment AB is parallel to DE and segment AC is parallel to DF, both shown with arrow marks. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Parallel lines cut by the transversal EF give equal corresponding angles.

Hint 2

Find the full length EF first.

Hint 3

Set up the ratio of corresponding sides of the similar triangles.

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 $△ A B C$ and $△ D E F$ :
$A B ∥ D E \Rightarrow ∠ A B C = ∠ D E F$ [corresponding angles]
$A C ∥ D F \Rightarrow ∠ A C B = ∠ D F E$ [corresponding angles]
$∴ △ A B C \sim △ D E F$ [AA similarity criterion]
1 mark
$E F = E B + B C + C F = 5 + 10 + 5 = 20$ cm. Corresponding sides of similar triangles are proportional: $\frac{B C}{E F} = \frac{A B}{D E} \Rightarrow \frac{10}{20} = \frac{7}{D E}$
½ mark
$D E = \frac{7 \times 20}{10} = 14$ cm
½ mark

Answer: $△ A B C \sim △ D E F$ (AA); DE = 14 cm

Where the marks are

Shows two pairs of equal angles from the parallel lines and concludes similarity by AA (1 mark)
Writes $\frac{B C}{E F} = \frac{A B}{D E}$ with $E F = 20$ cm (½ mark)
Gets DE = 14 cm (½ 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 paper2026 board paper, set 30/5/1 (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 2026: question 23

Hints

Step-by-step solution

Revise the chapter

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