To help you find the measure of segment $EF$, I'll need some context about the problem or the shape you are dealing with. Generally, to find the length of a segment like $EF$, we use different methods depending on the geometric figure or the given information. Here are some common scenarios:

1. On a Coordinate Plane:

If $E$ and $F$ are points on a coordinate plane with coordinates $E(x_1, y_1)$ and $F(x_2, y_2)$, you can find the length of $EF$ using the distance formula: $EF = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

2. In a Triangle:

If $EF$ is a side of a triangle, you can use various properties:

• Pythagorean Theorem: If the triangle is a right triangle, and $EF$ is either the hypotenuse or one of the legs, you can apply $a^2 + b^2 = c^2$.
• Law of Cosines: For any triangle, if you know the measures of the two other sides and the angle between them, use the formula: $EF^2 = a^2 + b^2 - 2ab \cos(C)$ where $a$ and $b$ are the other sides and $C$ is the angle opposite side $EF$.

3. In a Polygon:

If $EF$ is a side of a regular polygon, the length can depend on the perimeter or other given measurements such as the radius of a circumscribed circle.

4. Using Similarity or Proportionality:

If triangles or other figures involving $EF$ are similar, you can use the ratio of corresponding sides.

5. Involving Circles:

If $EF$ is a chord, tangent, or secant related to a circle, you might need circle properties like the Power of a Point theorem, or properties of tangents and secants.

Can you provide more context or details on your specific problem?

If you have any other questions or need further explanations, feel free to ask! Here are some related questions you might find helpful:

1. How do I use the distance formula to find the length of a segment?
2. What is the Law of Cosines and when should I use it?
3. How do I find the length of a side in a triangle using the Pythagorean Theorem?
4. How do properties of similar triangles help in finding unknown segment lengths?
5. What are the formulas for finding chord lengths in a circle?

Tip: Always double-check if additional information is given in your problem that could help simplify the calculation (like symmetry or specific angle measures).