Let's analyze the problem step by step.

Key Information from the Diagram:

• Point E is the midpoint of $AB$. This means $AE = EB = \frac{1}{2} AB$.
• Point F is the midpoint of $CD$. This implies $CF = FD = \frac{1}{2} CD$.

We are tasked to determine which three statements are correct.

Analyzing Each Statement:

1. "CD is bisected by AB":
   This statement is false. $AB$ does not bisect $CD$; instead, point $F$ bisects $CD$. There is no indication in the figure or information given that $AB$ divides $CD$ into equal parts.

2. "CE + EF = FD":
   This statement is true.
   Since $F$ is the midpoint of $CD$, we know $CF = FD$. Additionally, $CE + EF = CF$ (as $E$ and $F$ lie on the same segment from $C$ to $D$). Thus, $CE + EF = FD$.

3. "AE = $\frac{1}{2} AB$":
   This statement is true because $E$ is the midpoint of $AB$. By definition, $AE = EB = \frac{1}{2} AB$.

4. "EF = $\frac{1}{2} ED$":
   This statement is false. $EF$ is not half of $ED$. Instead, $EF = CF = FD = \frac{1}{2} CD$, but there is no relationship given between $EF$ and $ED$ as a whole.

5. "AB is bisected by CD":
   This statement is false. There is no indication that $CD$ bisects $AB$. The only bisection mentioned is $E$, which divides $AB$ into two equal parts.

Correct Answers:

The three true statements are:

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

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Related Questions:

1. What is the significance of a midpoint in geometric problems?
2. How can we confirm segment equality using midpoint properties?
3. How do bisections differ from midpoints in geometry?
4. Why does $AB$ not bisect $CD$ in the given diagram?
5. Can the relationships between segments like $EF$ and $ED$ be derived in other contexts?

Tip: Always carefully analyze the definitions of midpoint and bisection when solving geometric problems.