Question

what is df? df =

Explanation:

Step1: Recognize perpendicular - bisector property

Since the line is a perpendicular - bisector of $DF$ (as indicated by the right - angle and equal segments on the sides of the triangle), any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects. Here, point $E$ is on the perpendicular bisector of $DF$. So, $EF = ED$.

Step2: Determine the length of $DF$

We know that $FG = 3$ and the perpendicular bisector divides $DF$ into two equal parts. So, $DF=2\times FG$.
$DF = 2\times3=6$

Answer:

$6$