2025 · Basic · Set 6 · Part 1·Q22·2 marks
Triangles
Question
In a trapezium ABCD, and its diagonals intersect at O. Prove that .
Approach
In triangles OAB and OCD, ∠AOB = ∠COD (vertically opposite) and ∠OAB = ∠OCD (alternate angles since AB ∥ DC). By AA similarity, △OAB ∼ △OCD. Hence corresponding sides are proportional: OA/OC = OB/OD.
Step-by-step working
- 1
Proving (By AA similarity criterion)
1.5 marks - 2
(corresponding sides of similar triangles are proportional)
0.5 marks
Concepts used
trapeziumsimilar trianglesproportional sidesaa similarity
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