Question

In figure 5.40. AABC is an equilateral traingle.
Points FD and E are midpoints of side AB, side
BC, side AC respectively. Show that A FED is
an equilateral traingle.
Fig. 5.40​

Answer 1

Answer:

Step-by-step explanation:

Given ∆ABC is an equilateral triangle and D , E ans F are mid-points of BC , AC and AB respectively.

TO PROVE : ∆FED is an equilateral triangle.

Proof :

Since D and E are mid-points of BC and AC respectively.

DE = 1 / 2 AB ………...(i)

[By mid point theorem ,the line segment joining the mid-points of two sides of a triangle is half of the third side. ]

Similarly ,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

[From eq (i) , (ii) , (iii) ]

Hence, ∆FED is an equilateral triangle .