Question

In an equilateral triangle ABC the mid pt of
the side BC ,AB,CA is D , E , F
resp. prove that A DEF Is an equilateral triangle​

Answer 1

Answer:

Since line segment joining the mid-points of two sides of a triangle is half of the third side. Therefore, D and E are mid-points of BC and AC respectively. 

⇒ DE = 1 / 2 AB --- (i) 

E and F are the mid - points of AC and AB respectively .

∴ EF = 1 / 2 BC  --- (ii)

F and  D are the mid - points of AB and BC respectively .

∴ FD = 1 / 2 AC --- (iii)

Now, △ABC is an equilateral triangle .

⇒ AB =  BC = CA 

⇒ 1 / 2 AB = 1 / 2 BC = 1 / 2 CA  

⇒ DE = EF = FD [using (i) , (ii) , (iii) ]

Hence, DEF is an equilateral triangle .

Answer 2

Answer:

Prove that triangle DEF is an equilateral triangle

 In equilateral triangle ABC, the mid-points of sides BC,CA and AB are respectively D,E and F. Prove that triangle DEF is an equilateral triangle.

Step-by-step explanation:

plz mark me as

brainalist...