Question

in triangle ABC  D,E,F ARE MID POINTS OF SIDES AB, BC AND CA show that abc is divided  into 4 congruent triangles 

Answer 1

Lets say ABC is the triangle and D is the midpoint of AB , E is the mid point of AC and F be the mid point of BC.

so, AD=DB, AE=EC, BF=FC

if you draw a figure you will find that line segment DF is parallel to the line EC.

so EC=DF and similarly EF=AD then DE=FC also

the theorem proved by the definition of conjugate triangles.

Answer 2

Lets say ABC is the triangle and D,E and F are the midpoint of AB, AC and BC respectively

Therefore, AD=DB, AE=EC, BF=FC

line segment DF // EC.

so EC=DF 
similarly EF=AD
 DE=FC also

the theorem proved by the definition of conjugate triangles.