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In the given Figure, ABCD, DCFE and ABFE are parallelograms. S

Question

In the given Figure, $A BC D, D CFE$ and $A BFE$ are parallelograms. Show that $a r (A D E) = a r (BCF)$ .

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Emma Discussed

In the given Figure,

A BC D, D CFE

and

A BFE

are parallelograms. Show that

a r (A D E) = a r (BCF)

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

Since

A BC D

is a parallelogram, therefore sides

A D

and

BC

are equal.

Since

D CFE

is also a parallelogram, therefore, sides

D E

and

FC

are equal.

Since

A BFE

is also a parallelogram, therefore, sides

A E

and

BF

are equal.

So, triangles

A D E

and

BCF

are congruent by

SSS

congruency rule.

∴

Corresponding angles are equal in both triangles

So, the areas will be equal.

Therefore

a r (A D E) = a r (BCF)

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Question Text	In the given Figure, $A BC D, D CFE$ and $A BFE$ are parallelograms. Show that $a r (A D E) = a r (BCF)$ .
Answer Type	Text solution:1
Upvotes	150

In the given Figure, ABCD,DCFE and ABFE are parallelograms. Show that ar(ADE)=ar(BCF).

Text solutionVerified

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In the given Figure, $A BC D, D CFE$ and $A BFE$ are parallelograms. Show that $a r (A D E) = a r (BCF)$ .