Answer:
[tex]DE=4[/tex]
Step-by-step explanation:
We have been provided a graph of a triangle and we are asked to find the length of segment DE.
Angle bisector theorem states that if a ray bisects an angle of a triangle, then it bisects the opposite side of triangle into segments that are proportional to other two sides.
By angle bisector theorem we can set proportions of the given sides as:
[tex]\frac{DE}{EK}=\frac{DF}{FK}[/tex]
Upon substituting our given values in above proportion we will get,
[tex]\frac{DE}{2}=\frac{10}{5}[/tex]
Upon multiplying both sides of our equation by 2 we will get,
[tex]\frac{DE}{2}\times 2=2\times \frac{10}{5}[/tex]
[tex]DE=2\times 2[/tex]
[tex]DE=4[/tex]
Therefore, the length of segment DE is 4 units.
