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ABCD is a trapezium with AB DC. A line parallel to AC interse

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$A BC D$ is a trapezium with $A B ∥ D C$ . A line parallel to $A C$ intersects $A B$ at $X$ and $BC$ at $Y$ . Prove that $a r (△ A D X) = a r (△ A C Y)$

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A BC D

is a trapezium with

A B ∥ D C

. A line parallel to

A C

intersects

A B

X

and

BC

Y

. Prove that

a r (△ A D X) = a r (△ A C Y)

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given :

A BC D

is a trapezium with

A B ∥ D C

and

X Y ∥ A C .

Join

Y A, XC

and

X D .

Triangles

A CX

and

A C Y

have same base

A C

and are between same parallels

A C

and

X Y

So, $a r (△ A CX) = a r (△ A C Y)$ ......(i)

Triangles $A CX$ and $A D X$ have same base $A X$ and are between same parallels $A B$ and $D C .$

So, $a r (△ A CX) = a r (△ A D X)$ ......(ii)

From (i) and (ii),

$a r (△ A D X) = a r (△ A C Y)$

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Question Text	$A BC D$ is a trapezium with $A B ∥ D C$ . A line parallel to $A C$ intersects $A B$ at $X$ and $BC$ at $Y$ . Prove that $a r (△ A D X) = a r (△ A C Y)$
Answer Type	Text solution:1
Upvotes	150

ABCD is a trapezium with AB∥DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar(△ADX)=ar(△ACY)

Text solutionVerified

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$A BC D$ is a trapezium with $A B ∥ D C$ . A line parallel to $A C$ intersects $A B$ at $X$ and $BC$ at $Y$ . Prove that $a r (△ A D X) = a r (△ A C Y)$