Mathematics
In the adjoining figure, DE ∥ BC. Prove that :
(i) ar (ΔABE) = ar (ΔACD)
(ii) ar (ΔOBD) = ar (ΔOCE)
Theorems on Area
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Answer
(i) We know that,
Triangles on the same base and between the same parallel lines are equal in area.
∆BCD and ∆BCE are on the same base BC and between the same || lines DE and BC.
⇒ Area of ∆BCD = Area of ∆BCE
Subtracting area of ∆BCD and ∆BCE from area of ∆ABC
⇒ Area of ∆ABC - Area of ∆BCD = Area of ∆ABC - Area of ∆BCE
⇒ Area of ∆ACD = Area of ∆ABE.
Hence proved, that area of ∆ACD = area of ∆ABE.
(ii) We know that,
⇒ Area of ∆BCD = Area of ∆BCE
Subtracting area of ∆OBC from above equation we get,
⇒ Area of ∆BCD - Area of ∆OBC = Area of ∆BCE - Area of ∆OBC
⇒ Area of ∆OBD = Area of ∆OCE.
Hence proved, that area of ∆OBD = area of ∆OCE.
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