Question

in triangle abc d e and f are midpoints of the sides Ab,bc and CA respectively show that ar(∆DEF)=1/4 ar(∆ABC)​

Answer 1

hope you can understand ✨

Answer 2

R.E.F image

As BDEF is a ∥gm

∴△DEF≅△DBF

⇒ar(DBF)=ar(DEF)

similarly, we can prove FDCE is ∥gm

∴△DEC≅△DEF

⇒ar(DEC)=ar(DEF)

similarly, we have prove AFDE is∥gm

∴△AFE≅△DEF

⇒ar(AFE)=ar(DEF)

so ar(FBD)=ar(DEC)=ar(AFE)=ar(DEF)

Now ar(FBD)+ar(DEC)+ar(AFE)+ar(DEF)=ar(ABC)

ar(DEF)+ar(DEF)+ar(DEF)+ar(DEF)=ar(ABC)

4ar(DEF)=ar(ABC)

ar(DEF)=¼ ar(ABC)

∴ Proved ✅