Question

parallelogram are on the same base and between the same parallels are eqaul in area show that.​

Answer 1

Theorem: Parallelograms on the same base and between the same parallels are equal in area. ... BC = AD (opposite sides of a parallelogram are equal)

Answer 2

Answer:

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.