In `DeltaA B C` , D, E and F are respectively the mid-points of sides AB, BC and CA. Show that `DeltaA B C` is divided into four congruent triangles by joining D, E and F.

Explanation

`D` is the midpoint of `AB`

`E` is the midpoint of `BC`
So according to midpoint theorem, `DE"//"AC`
Similarly, `DF"//"BC` and `EF"//"AB`

`therefore ADEF, BDFE and DFCE` are
parallelograms

`DE` is a diagonal of parallelogram,`BDFE`

`therefore /_\ BDE~= /_\ FED`

`similarly /_\DAF ~= /_\FED`

`/_\EFC~=/_\FED`

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