Question

Point E is the midpoint of Line segment A B and point F is the midpoint of Line segment C D .

3 intersecting lines are shown. A line has points C, E, F, D. Another line has points A, E, and B and intersects the other line at point E. Another line goes from point A to point F.
Which statements about the figure must be true? Select three options.

Line segment A B is bisected by Line segment C D .
Line segment C D is bisected by Line segment A B .
AE = One-halfAB
EF = One-halfED
CE + EF = FD

Answer 1

Correct choices:
- Line segment AB is bisected by line segment CD.
- AE = One-half AB.
- CE + EF = FD.

Reasoning (brief):
- E is the midpoint of AB and E lies on CD, so CD passes through the midpoint of AB → CD bisects AB.
- E is the midpoint of AB → AE = AB/2.
- C, E, F, D are collinear and F is the midpoint of CD, so CE + EF = CF and CF = FD, hence CE + EF = FD.

The other two statements need not be true (AB does not necessarily pass through F, and EF need not equal (1/2)ED).