MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic 2025: question 22

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section B, question 22, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22 · 2 marks · Very short answerTriangles

In a trapezium ABCD, AB $∥$ DC and its diagonals intersect at O. Prove that $\frac{O A}{O C} = \frac{O B}{O D}$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

Look for two triangles that have OA, OB in one and OC, OD in the other.

Hint 2

Since AB ∥ DC, the diagonals act as transversals: use alternate angles to show the triangles are similar.

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.

Draw trapezium ABCD with AB ∥ DC and diagonals AC and BD meeting at O.
In $△ O A B$ and $△ O C D$ :
$∠ O A B = ∠ O C D$ [alternate angles, AB ∥ DC, AC is a transversal]
$∠ O B A = ∠ O D C$ [alternate angles, AB ∥ DC, BD is a transversal]
Therefore $△ O A B \sim △ O C D$ [AA similarity criterion].
1½ marks
Corresponding sides of similar triangles are proportional, so $\frac{O A}{O C} = \frac{O B}{O D}$ . Hence proved.
½ mark

Answer: $△ O A B \sim △ O C D$ (AA), hence $\frac{O A}{O C} = \frac{O B}{O D}$

Where the marks are

Proves $△ O A B \sim △ O C D$ using alternate angles and the AA criterion (1½ marks)
Uses proportionality of corresponding sides to conclude $\frac{O A}{O C} = \frac{O B}{O D}$ (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 paper2025 board paper, set 430/6/1 (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 2025: question 22

Hints

Step-by-step solution

Revise the chapter

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