point e is the midpoint of $\overline{ab}$ and point f is the midpoint of $\overline{cd}$. which statements about the figure must be true? select three options. $\square$ $\overline{ab}$ is bisected by $\overline{cd}$. $\square$ $\overline{cd}$ is bisected by $\overline{ab}$. $\square$ $ae = \frac{1}{2}ab$ $\square$ $ef = \frac{1}{2}ed$ $\square$ $ce + ef = fd$

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# Brief Explanations:
1. For "AE = $\frac{1}{2}$AB": Since E is the midpoint of $\overline{AB}$, by the definition of a midpoint, $AE = EB=\frac{1}{2}AB$, so this is true.
2. For "EF = $\frac{1}{2}$ED": F is the midpoint of $\overline{CD}$, so $CF = FD$, but also, from the midpoint property and the segment relations, $EF=\frac{1}{2}ED$ (as F divides CD and E is a point such that the segment ED is split by F into two equal parts? Wait, no, F is midpoint of CD, but looking at the line CD, E is between C and F, F is midpoint of CD, so $CF = FD$, and $EF$ and $FD$: Wait, actually, since F is the midpoint of CD, $CF = FD$, and if we consider ED, $EF + FD=ED$, and since $FD = CF$, but also, from the midpoint of AB (E) and midpoint of CD (F), the segment EF: Wait, maybe better to re - evaluate. Wait, the key is:
   - E is midpoint of AB: so $AE = EB=\frac{1}{2}AB$ (true).
   - F is midpoint of CD: so $CF = FD$. Now, for $EF=\frac{1}{2}ED$: $ED=EF + FD$, and since $FD = CF$, but also, if we consider that on line CD, F is the midpoint, so $CF = FD$, and $EF$ and $FD$: Wait, maybe the third true statement is "CD is bisected by AB"? No, wait, the options: Let's re - check each option:
     - "AB is bisected by CD": CD intersects AB at E, and E is the midpoint of AB, so by definition, a segment is bisected by another segment if the second segment passes through the midpoint of the first. So CD passes through E (midpoint of AB), so AB is bisected by CD (true). Wait, earlier I thought of AE = 1/2 AB, and let's check the other options:
       - "AB is bisected by CD": Since E is the midpoint of AB and CD passes through E, AB is bisected by CD (true).
       - "AE=$\frac{1}{2}$AB": As E is midpoint of AB, this is true.
       - "EF=$\frac{1}{2}$ED": Since F is midpoint of CD, $CF = FD$, and $EF+FD = ED$, and since $FD=\frac{1}{2}CD$, but also, $EF=\frac{1}{2}ED$ (because F is the midpoint of CD, and E is a point on CD? Wait, no, E is on AB and CD? Wait, the figure shows that E is the intersection of AB and CD. So E is on CD and AB. So CD is a straight line with C---E---F---D, and F is the midpoint of CD, so $CF = FD$. Then $ED=EF + FD$, and since $FD = CF$, and $EF$ and $FD$: If we consider that F is the midpoint of CD, then $FD=\frac{1}{2}CD$, but also, $EF=\frac{1}{2}ED$ (because $EF$ and $FD$ are such that $FD = EF$? Wait, no, let's take an example: suppose CD = 4 units, so CF = FD = 2 units. Let CE = 1 unit, then EF = 1 unit, ED=EF + FD=1 + 2 = 3? No, that's not. Wait, maybe my initial thought was wrong. Wait, the correct true statements are:
     - "AE=$\frac{1}{2}$AB" (because E is midpoint of AB).
     - "CD is bisected by... Wait, the options:
       - Option 1: $\overline{AB}$ is bisected by $\overline{CD}$: Since E is the midpoint of AB and E lies on CD, so CD bisects AB (true).
       - Option 3: $AE=\frac{1}{2}AB$ (true, by midpoint definition).
       - Option 4: $EF=\frac{1}{2}ED$: Since F is the midpoint of CD, $CF = FD$, and on line CD, E---F---D, so $EF + FD=ED$, and since F is midpoint, $FD=\frac{1}{2}CD$, but also, $EF=\frac{1}{2}ED$ (because $FD = EF$? Wait, no, if F is midpoint of CD, and E is a point such that $EF=FD$, then $EF=\frac{1}{2}ED$ (because $ED = EF+FD$ and $EF = FD$). So this is true. Wait, maybe the three true options are: $\overline{AB}$ is bisected by $\overline{CD}$, $AE=\frac{1}{2}AB$, and $EF=\frac{1}{2}ED$? Wait, no, let's re - examine:
       - $\overline{AB}$ is bisected by $\overline{CD}$: E is midpoint of AB and E is on CD, so CD bisects AB (true).
       - $AE=\frac{1}{2}AB$: E is midpoint of AB, so true.
       - $EF=\frac{1}{2}ED$: F is midpoint of CD, so $CF = FD$, and since E is on CD (as AB and CD intersect at E), then $EF + FD=ED$, and since $FD = CF$, and if we consider that F is the midpoint, then $EF=\frac{1}{2}ED$ (because $FD = EF$). So these three are true? Wait, no, the option "CD is bisected by AB": AB intersects CD at E, but E is not the midpoint of CD (F is the midpoint of CD), so "CD is bisected by AB" is false.
       - So the correct three options are: $\overline{AB}$ is bisected by $\overline{CD}$, $AE=\frac{1}{2}AB$, and $EF=\frac{1}{2}ED$? Wait, no, let's check again:
         - E is midpoint of AB: $AE = EB=\frac{1}{2}AB$ (true).
         - F is midpoint of CD: $CF = FD$.
         - $\overline{AB}$ is bisected by $\overline{CD}$: Because CD passes through E, the midpoint of AB (true).
         - $EF=\frac{1}{2}ED$: Since F is midpoint of CD, $FD=\frac{1}{2}CD$, and $EF + FD=ED$, and if we assume that $EF = FD$ (from the figure's segment relations, as F is midpoint and E is a point such that the segment from E to F is equal to F to D), then $EF=\frac{1}{2}ED$ (true).
# Answer:
- $\overline{AB}$ is bisected by $\overline{CD}$
- $AE=\frac{1}{2}AB$
- $EF=\frac{1}{2}ED$

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