Question

prove that the line segment joining the middle point of the side of triangle divides into four congruent triangles

Answer 1

given: ABC is a triangle. D, E and F are the mid-points of the sides BC, CA and AB respectively.

TPT:

proof:

by the mid-point theorem:

therefore FEDB is a parallelogram.

since the diagonal of a parallelogram divides it into two congruent triangles.

therefore ........(1)

similarly FECD is a parallelogram.

and ED diagonal divides it into two congruent triangles.

.............(2)

from (1) and (2):



similarly we can show that

hope this helps you.

cheers!!

Answer 2

According to mid point theorem,
AD=BD=EF
AE=CE=DF
BF=CF=DE

In Δ ADE and Δ FED
AD=FEBRUARY
AE=FD
DE=ED
Δ ADE is congruent to Δ FED
Similarly others can be proved
Thus all 4 triangles are congruent