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CBSE Class 9 Answered

In triangle ABD, D, E and F are mid-points of sides AB, BC and CA respectively. Show that ABC is divided into four congruent triangles by joining D, E and F.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

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.

Answered by | 04 Jun, 2014, 03:23: PM

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