डेवलप a डायलॉग बिटवीन यू एंड योर मदर ऑन द सेलिब्रेशन ऑफ रिपब्लिक डे इन योर स्कूल
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Answer:
D and E are mid-points of sides BC and AC respectively.
So, DE∥BA⟹DE∥BF
Similarly, FE∥BD. So, BDEF is a parallelogram.
Similarly, DCEF and AFDE are parallelograms.
Now, DF is a diagonal of parallelogram BDEF.
Therefore,
ar(△BDF)=ar(△DEF) .....(1)
DE is a diagonal of parallelogram DCEF.
So, ar(△DCE)=ar(△DEF) .....(2)
FE is a diagonal of parallelogram AFDE.
ar(△AFE)=ar(△DEF) ....(3)
From 1,2 &3, we have,
ar(△BDF)=ar(△DCE)=ar(△AFE)=ar(△DEF)
But, ar(△BDF)+ar(△DCE)+ar(△AFE)+ar(△DEF)=ar(△ABC)
So, 4ar(△DEF)=ar(△ABC)
ar(△DEF)=
4
1
ar(△ABC)
Now, ar(∥
gm
BDEF)=2ar(△DEF)
ar(∥
gm
BDEF)=2×
4
1
ar(△ABC)=
2
1
ar(△ABC)
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