The statements for the line AB and CD for this condition that are true are given as:
Option A: [tex]\overline{AB}[/tex] is bisected by [tex]\overline{CD}[/tex]
Option C: [tex]AE = \dfrac{1}{2} \times AB[/tex]
Option F: CE + EF = FD
What is a bisector?
A bisector of a line bisects that considered line. Bisect means to split in two equal parts.
For this case, we see that CD passes through mid point of AB, so CD is bisector of line AB or we say that line segment AB is bisected by line segment CD.
But AB does not passes through the center of AB, thus, AB is not a bisector of CD, or we say that line segment CD is not bisected by line segment AB
AE = EB
And AE + EB = AB
Thus, AE + AE + AB
or 2AE = AB
or AE = (AB)/2 = (1/2)AB
E is not necessary to be fixed on CD, it can move between C and F. Thus any statement about length of E to any point on CD is not necessary to be true.
FD is half of CD and EB is half of AB. It is not necessary that AB and CD are of same length, thus, it is not necessary that FD and EB are going to be of same length, thus, not congruent(two line segments are called congruent (denoted by ≅) if they are of same lengths).
CE + EF = CF, and CF = FD since F is midpoint.
Thus, CE + EF = FD
Thus, the statements for the line AB and CD for this condition that are true are given as:
Option A: [tex]\overline{AB}[/tex] is bisected by [tex]\overline{CD}[/tex]
Option C: [tex]AE = \dfrac{1}{2} \times AB[/tex]
Option F: CE + EF = FD
Learn more about bisecting lines here:
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