Question

plzz answer the 6th one

Answer 1

Hi friend,

Given: ar( llgm ABCD)=ar( llgm AGFE)

To prove: DGllFC

Construction: Join DF and GC

Proof:
let FG and DC intersect at O.
since , ar( ABCD)= ar( AGFE)
ar( ABCD) - ar( AGOD)= ar( AGFE) - ar( AGOD)
ar(BGOC) = ar( DOFE)
1/2 ar( BGOC) = 1/2 ar( DOFE)
ar (∆DOF)= ar(∆ GOC)
ar( ∆DOF) + ar(∆FOC)= ar( ∆GOC)+ ar( ∆FOC)
ar(∆ DFC) = ar( ∆GCF)
Since these two triangles lie on the same base FC and have the same area .
therefore, DGIIFC.
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