point e is the mid - point of $overline{ab}$ and point f is the mid - point of $overline{cd}$. which…

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

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

Answer

Explanation:

Step1: Recall mid - point definition

A mid - point of a line segment divides the line segment into two equal parts. Since E is the mid - point of $\overline{AB}$, by the definition of a mid - point, $AE = EB=\frac{1}{2}AB$. So, $AE=\frac{1}{2}AB$ is true.

Step2: Analyze the relationship of line segments based on mid - points

Since F is the mid - point of $\overline{CD}$, we have $CF = FD$. Also, $CF=CE + EF$. So, $CE + EF=FD$ is true.

Step3: Check bisection statements

There is no information given to suggest that $\overline{AB}$ is bisected by $\overline{CD}$ or $\overline{CD}$ is bisected by $\overline{AB}$. And there is no information to support $EF=\frac{1}{2}ED$.

Answer:

$AE=\frac{1}{2}AB$, $CE + EF = FD$