Question

prove that parallelograms on the same base and between the same parallel are equal in area​

Answer 1

Given two parallelogram ABCD and EFCD that have the same base CD and lie between same parallel AF and CD.

We have prove that ar(ABCD)=ar(EFCD)

Since opposite sides of ∥gm are parallel AB∥CD and ED∥FC with transversal AB

⇒∠DAB=∠CBF [ Corresponding angles ]

with transversal EF

⇒∠DEA=∠CFE [ Corresponding angles ]

⇒AD=BC [ Opposite sides of parallelogram are equal ]

In △AED ξ △BFC

⇒∠DEA=∠CFE

∠DAB=∠CBF

∴AD=BC

⇒△AED≅△BFC [ AAS congruency ]

Hence, ar(△AED)=ar(△BFC)

( Areas of congruent figures are equal )

⇒ar(ABCD)=ar(△ADE)+ar(EBCD)

=ar(△BFC)+ar(EBCD)

=ar(EBCD)

∴ar(ABCD)=ar(EBCD)

Hence, the answer is proved.

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