Question

Parallelograms on the same base and between the same parallels are equal in (a) perimeter (b) volume (c) area (d) weight

Answer 1

$\huge\green{Answer}$⇒Here, two parallelograms ABCD and EFCD, that have the same base CD and lie between same parallels AF and CD.

Since opposite sides of parallelogram are parallel

AD∥BC with transversal AB

⇒  ∠DAB=∠CBF     [ Corresponding angles ]     ----- ( 1 )

ED∥FC with transversal EF

⇒  ∠DEA=∠CFE     [ Corresponding angles ]     ----- ( 2 )

In △AED and △BFC

⇒  ∠DEA=∠CFE               [ From ( 2 ) ]

⇒  ∠DAB=∠CBF              [ From ( 1 ) ]

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

∴  △AED≅△BFC        [ AAS congruence property ]

⇒  ar(△AED)=ar(△BFC)        [ Area of congruent figures are equal ]

Adding ar(EBCD) on both sides,

⇒  ar(△AED)+ar(EBCD)=ar(△BFC)+ar(EBCD)

⇒  ar(ABCD)=ar(EFCD)  

∴  The parallelogram based upon the same base and between the same parallel lines are equalinarea

$\huge\orange{@alurringbabe}$

Answer 2

parallelograms on the same base and between the same parallels are equal in area.