CBSE Class 10 Mathematics Standard 2024: question 24
Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, section B, question 24, for 2 marks. Try it first; the hints and our step-by-step solution are below.
Q24 · 2 marks · Very short answerTriangles
In the given figure, , prove that .
Figure in the paper: Two line segments AC and BD intersect at point E inside, forming triangles EAB and ECD. A is at upper left, B at lower left, C at lower right, D at upper right. E is the intersection point of AC and BD. See it in the official paper.
Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.
Hints
Open one hint at a time and try again before the next.
Hint 1
You already have two sides in proportion. What do you need between them?
Hint 2
Look at the angles at E formed by the crossing lines AC and BD.
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 and : [given].
- 1 mark
[vertically opposite angles, since AC and BD cross at E].
- 1 mark
Two sides are in the same ratio and the included angles are equal, so [SAS similarity criterion].
Answer: △EAB ~ △ECD by the SAS similarity criterion
Where the marks are
- States the given ratio and as vertically opposite angles (1 mark)
- Concludes similarity by SAS criterion (1 mark)
Revise the chapter
- Chapter: Triangles (notes, formulas, where marks are lost and every past question)
- Topic: Problems on Similar Triangles
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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.