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in Parallelograms by (58.8k points)

In the adjoining figure, DE || BC. Prove that

(i) ar (△ ACD) = ar (△ ABE)

(ii) ar (△ OCE) = ar (△ OBD).

1 Answer

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Best answer

(i) From the figure we know that △ DBE and △ DCE lie on the same base DE between the parallel lines BC and DE.

So we get

Area of △ DBE = Area of △ DCE ……. (1)

By adding △ ADE both sides

Area of △ DBE + Area of △ ADE = Area of △ DCE + Area of △ ADE

We get

Area of △ ABE = Area of △ ACD

Therefore, it is proved that ar (△ ACD) = ar (△ ABE).

(ii) Subtracting △ ODE from equation (1)

We get

Area of △ DBE – Area of △ ODE = Area of △ DCE – Area of △ ODE

We get

Area of △ OBD = Area of △ OCE

Therefore, it is proved that ar (△ OCE) = ar (△ OBD).

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