Answer
equilateral triangle
Work Step by Step
D(0,0) E(4,0) and F(2,2$\sqrt 3$)
Using distance formula
x1=0,y1=0,x2=4,y2=0
then, $\overline{DE}$ = $\sqrt (x2-x1)^{2} + (y2-y1)^{2}$
= $\sqrt (4-0)^{2} + (0-0)^{2}$
=4 units
Similarly,
$\overline{EF}$ = $\sqrt (2-4)^{2} + (2\sqrt 3-0)^{2}$
=$\sqrt 2^{2} + 2\sqrt 3^{2}$ = $\sqrt 4+12$ = $\sqrt 16$ =4 units
$\overline{FD}$ = $\sqrt (2-0)^{2} + (2\sqrt 3-0)^{2}$
=$\sqrt 2^{2} + 2\sqrt 3^{2}$ = $\sqrt 4+12$ = $\sqrt 16$ =4 units
Therefore $\overline{DE}$ = $\overline{EF}$ =$\overline{FD}$ in triangle DEF
therefore triangle DEF is equilateral triangle.