The correct three options are -
- Line segment AB is bisected by Line segment CD.
- [tex]AE = \frac{1}{2} AB[/tex].
- [tex]CE + EF = FD[/tex]
What is Midpoint?
The midpoint of a line segment is a point situated on a line segment at which the line segment is divided into two equal lengths.
What is a Bisector?
The bisector is a line segment which cuts another line segment into two parts of equal length.
Here in the problem, we have -
E is the midpoint of Line segment AB and point F is the midpoint of Line segment CD.
A line has points C, E, F, and D.
Another line has points A, E, and B.
A line goes from point A to point F.
So from the figure we can see that Line segment CD intersects Line segment AB at point E and E is the midpoint of AB. So clearly CD bisects AB.
So option (a) is correct.
F is the midpoint of CD but AB intersects CD at E which is situated left of F then AB does not bisect the line segment CD.
So option (b) is incorrect.
As E is the midpoint of AB so it divides the line into equal two parts.
[tex]AE = EB = \frac{1}{2}AB[/tex]
So option (c) is correct.
F is the midpoint of CD.
So, [tex]CF = FD = \frac{1}{2} CD[/tex]
Hence, EF is not one-half ED as we don't know about the midpoint of ED.
Thus, option (d) is incorrect.
From the figure, we can see that,
[tex]CE + EF = CF[/tex]
and F is the midpoint of CD
[tex]CF = FD\\CE + EF = FD[/tex]
Hence option (e) is correct.
Learn more about Mid-point here -
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