CBSE Class 10 Mathematics Standard sample paper 2026-27: question 22(A)
From the official CBSE sample question paper for 2026-27, 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
ABCD is a trapezium in which AB is parallel to DC and its diagonals intersect each other at the point O. Show that .
Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.
Hints
Open one hint at a time and try again before the next.
Hint 1
AB ∥ DC: look for alternate angles along the diagonals.
Hint 2
Prove triangles AOB and COD 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.
- 1 mark
In and : and [alternate interior angles, with transversals AC and BD].
- ½ mark
[AA similarity criterion].
- ½ mark
Corresponding sides are proportional, so . Hence . Hence proved.
Answer: (AA), hence
Where the marks are
- Two pairs of equal alternate angles with reason (1 mark)
- States ΔAOB ~ ΔCOD by AA (½ mark)
- Writes the proportion and rearranges to the result (½ mark)
Revise the chapter
- Chapter: Triangles (notes, formulas, where marks are lost and every past question)
- Topic: Basic Proportionality Theorem (Thales Theorem)
More questions from Triangles
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- 2026 board paper, set 30/1/1 (Standard), Q22(A) · 2 marksIn Δ ABC, DE ∥ BC. If AD = x, DB = x - 2, AE = x + 2 and EC = x - 1, then find the value of x.
- 2026 board paper, set 30/1/1 (Standard), Q34(A) · 5 marksState and prove Basic Proportionality Theorem.
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