Please solve question no.3.
Given that D, E and F are the mid points of sides AB, BC, CA respectively.
To show: ΔABC is divided into four congruent triangles
Proof: D is the mid point of AB
F is the mid point of AC.
∴DF||BC (By mid point theorem)
also E is the mid point of BC
and F is the mid point of AC.
∴EF||AB (By mid point theorem)
By (1) & (2)
BEFD is a parallelogram
⇒ΔBDEΔDEF (Since diagonal of a parallelogram divides it into two congruent triangles) ......(3)
By (3), (4) & (5)
ΔABC is isosceles . Therefore, AB = AC ......(1)
D is the mid point of AB
E is the mid point of BC.
∴DE||BC and DE = AC/2 (By mid point theorem) .......(2)
F is midpoint of AC
E is the midpoint of BC
So, EF||AC and EF= AB/2 (By mid point theorem) .......(3)