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Standard VIII

Mathematics

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ABCD is a tra...

Question

$A B C D$ is a trapezium in which $A B ∥ D C$ is produced to $E$ such that $C E = A B$ . Prove that $a r (Δ A B D) = a r (Δ B C E)$

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Solution

Given :
$A B ∥ C D,$ then $A B ∥ C E$ and
$C E = A B$
$∴$ $A B E C$ is a parallelogram.
It is known that diagonal of parallelogram bisect it into two triangles of equal area.
$∴$ $a r (△ A B C) = a r (△ B C E)$ ---- ( 1 )
$△ A B D$ and $△ A B C$ lie on the same base $A B$ and between same parallels $A B$ and $D C$ .
$∴$ $a r (△ A B C) = a r (△ A B D)$ ----- ( 2 )
From equations ( 1 ) and ( 2 )
$∴$ $a r (△ A B D) = a r (△ B C E)$

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ABCD is a trapezium in which AB∥DC is produced to E such that CE=AB. Prove that ar(ΔABD)=ar(ΔBCE)

$A B C D$ is a trapezium in which $A B ∥ D C$ is produced to $E$ such that $C E = A B$ . Prove that $a r (Δ A B D) = a r (Δ B C E)$