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Triangles
CBSE 2026 Board Exam Set 1 (Code 30/1/1)
CBSE_BOARD_PYQ_2026_30_1_1
Grade 10
Question:
[Section C]
$ABCD$ is a trapezium with $AB \parallel DC$. Diagonals $AC$ and $BD$ intersect at $O$. Show that $\dfrac{AO}{BO} = \dfrac{CO}{DO}$.
$ABCD$ is a trapezium with $AB \parallel DC$. Diagonals $AC$ and $BD$ intersect at $O$. Show that $\dfrac{AO}{BO} = \dfrac{CO}{DO}$.
Step-by-Step Solution
Key Concept: $\triangle AOB \sim \triangle COD$ by AA similarity (alternate interior angles).
In $\triangle AOB$ and $\triangle COD$, $\angle OAB = \angle OCD$ and $\angle OBA = \angle ODC$. [1.5 Marks]
$\triangle AOB \sim \triangle COD \Rightarrow AO/CO = BO/DO \Rightarrow AO/BO = CO/DO$. Hence proved. [1.5 Marks]
$\triangle AOB \sim \triangle COD \Rightarrow AO/CO = BO/DO \Rightarrow AO/BO = CO/DO$. Hence proved. [1.5 Marks]
Correct Answer: Proof shown via AA similarity.
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