In the figure, D and E are two poins on BC such that BD = De = EC. Show that ar $(△ A B D) = a r (△ A D E) = a r (△ A E C) .$

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Solution

Given: D and E are two points on such that BD = DE = EC
Ad and AE are joined
To prove : ar $(△ A B D) = a r (△ A D E) = a r (△ A E C)$
Construction: From A, draw $A L ⊥ B C$ and XAY || BC

Proof: $∵$ BD = DE = EC
and $△ A B D, △ A D E a n d △ A E C$ have equal bases and from the common vertex A

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