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# Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC). - CBSE Class 9 - Mathematics

ConceptTriangles on the Same Base and Between the Same Parallels

#### Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

#### Solution It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.

∴ Area (ΔDAC) = Area (ΔDBC)

⇒ Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)

⇒ Area (ΔAOD) = Area (ΔBOC)

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#### APPEARS IN

NCERT Solution for Mathematics Class 9 (2018 to Current)
Chapter 9: Areas of Parallelograms and Triangles
Ex. 9.30 | Q: 10 | Page no. 163

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Solution Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC). Concept: Triangles on the Same Base and Between the Same Parallels.
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