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D, E and F are respectively the mid-poin...

D, E and F are respectively the mid-points of sides AB. BC and CA of `triangleABC`. Find the ratio of the areas of `triangleDEF` and `triangleABC`.

Text Solution

Verified by Experts

`AD=DB=1/2AB`
`AF=FC=1/2AC`
from these two equations
`(AD)/(AB)=(AF)/(AC)=(DF)/(BC)=1/2`
`angleBAC=angleDAF`
SAS Similarity
`/_ABC`~`/_ADF`
`(DE)/(AC)=(EF)/(AB)=(FD)/(BC)=1/2`
...
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