Question

in triangle ABC, D, E and F are the mid points of sides AB, BC and CA respectively. show that triangle ABC is divided into four congruent triangles, when three mid points are joined to each other

Answer 1

As D and E are mid-points of sides AB and BC of the triangle ABC, by Theorem 1,

DE || AC

Similarly, DF || BC and EF || AB

Therefore ADEF, BDFE and DFCE are all parallelograms.

Now DE is a diagonal of the parallelogram BDFE,

 therefore, ∆ BDE ≅ ∆ FED

Similarly ∆ DAF ≅ ∆ FED

and ∆ EFC ≅ ∆ FED

So, all the four triangles are congruent.

Answer 2

Answer:

Step-by-step explanation:

As D and E are mid-points of AB and BC of ABC,

DE||AC

Similarly DF||BC, EF||AB

ADEF, BDFE and DFCE are all parallelograms.

DE is the diagonal of the parallelogram BDFE.

(Since, a diagonal of a parallelogram divides it into two congruent triangles)

Similarly, and

Thus, all the four triangles, BDE, FED, EFC and DAF, are congruent