Question

Prove that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.
Please Answer ​

Answer 1

Angle F and E are the midpoints of AB and AC.
From the midpoint theorem
EF=1/2BC

Similarly,
FD= 1/2 AC
ED=1/2AB
In △AFE and △BFD,
AF=FB
From the midpoint theorem,
FE=1/2 BC=BD
FD=1/2AC=AE


△AFE ≅ △BFD———————(By SSS test of congruence)

In △BFD AND △FED,
FE=BC


Therefore,□BDEF Is a quadrilateral.
So now, FD Is a diagonal which divides the parallelogram into two congruent triangles.

△BFD≅△FED

□FECD is a parallelogram

△FED≅△EDC
So, △BFD,△FDE,△FED and △EDC are congruent to each other

Therefore, it is proved that the line segments joining the middle points of the sides of a triangle divide it into four congruent triangles.