Question

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

Answer 1

Answer:

This theorem from areas related to circle gr 10

Answer 2

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

To prove:- ar(ABCD)=ar(EFCD)

Proof:-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.