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in Parallelograms by (65.5k points)

In Fig., ABCD, DCEF and ABFE are parallelograms. Show that ar. (∆ADE) = ar. (∆BCF).

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Data : ABCD, DCEF and ABFE are Parallelograms. 

To Prove: ar.(∆ADE) = ar.(∆BCF) 

Proof: In ABCD, 

∴ AD = BC (Opposite sides of ) ………… (i) 

Similarly, in DCFE, DE = CF (Opposite sides of ) ………..(ii) 

Similarly, in ABFE, AE = BF (Opposite sides of ) ………… (iii) 

In ∆ADE and ∆BCF, AD = BC ……… (1) 

DE = CF ……… (2) 

AE = BF ……… (3) 

∴ ∆ADE ≅ ∆BCF (SSS postulate) 

∴ ar.(∆ADE) = ar.(∆BCF).

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