MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 22(a)

From the official CBSE sample question paper for 2023-24, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerTriangles

In the given figure, if ABCD is a trapezium in which $A B ∥ C D ∥ E F$ , then prove that $\frac{A E}{E D} = \frac{B F}{F C}$ .

Figure in the paper: Trapezium ABCD with AB at the bottom and DC at the top, AB parallel to DC. Points E lie on AD (left slanted side) and F lie on BC (right slanted side). A line EF is drawn parallel to AB and DC, crossing the two non-parallel sides. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

A trapezium is not a triangle. Draw a diagonal to create two triangles.

Hint 2

Join BD, cutting EF at G, and apply the Basic Proportionality Theorem in each of the two 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.

Construction: Join diagonal $B D$ ; let it cut $E F$ at $G$ .
½ mark
In $△ A B D$ , $E G ∥ A B$ [since $E F ∥ A B$ ]. By BPT, $\frac{A E}{E D} = \frac{B G}{G D}$ ...(1)
½ mark
In $△ D B C$ , $GF ∥ D C$ [since $E F ∥ C D$ ]. By BPT, $\frac{B F}{F C} = \frac{B G}{G D}$ ...(2)
½ mark
From (1) and (2), $\frac{A E}{E D} = \frac{B F}{F C}$ . Hence proved.
½ mark

Answer: $\frac{A E}{E D} = \frac{B F}{F C}$ proved using BPT in $△ A B D$ and $△ D B C$

Where the marks are

Construction: join BD meeting EF at G (1/2 mark)
BPT in $△ A B D$ gives $\frac{A E}{E D} = \frac{B G}{G D}$ (1/2 mark)
BPT in $△ D B C$ gives $\frac{B F}{F C} = \frac{B G}{G D}$ (1/2 mark)
Equates the two ratios to conclude (1/2 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 paperSample paper 2023-24 (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 sample paper 2023-24: question 22(a)

Hints

Step-by-step solution

Revise the chapter

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