In the given figure, XY || BC, BE || CA and FC || AB. Prove that : ar (ΔABE) = ar (ΔACF).
Theorems on Area
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Question

In the given figure, XY || BC, BE || CA and FC || AB. Prove that : ar (ΔABE) = ar (ΔACF).

KnowledgeBoat · Accepted Answer

Parallelograms BCYE and BCFX stand on the same base BC and lie between the same parallels BC and XY. ar (∥ gm BCYE) = ar (∥ gm BCFX) = x (let) .....(1) Δ ABE shares the base BE with parallelogram BCYE and lies between the same parallels BE and AC. ar (Δ ABE) = ar (∥ gm BCYE) = .....(2) Δ ACF shares the base CF with parallelogram BCFX and lies between the same parallels CF and AB. ar (Δ ACF) = ar (∥ gm BCFX) = .....(3) From equation (2) and (3), we get : ar (Δ ABE) = ar (Δ ACF) Hence, proved that ar (Δ ABE) = ar (Δ ACF).

Mathematics

In the given figure, XY || BC, BE || CA and FC || AB. Prove that : ar (ΔABE) = ar (ΔACF).

Theorems on Area

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