Classify geometric figures as lines, rays, or line segments and write their names.
Check the final answer first, then review the worked steps.
Problem
Classify geometric figures as lines, rays, or line segments and write their names.
Answer
(a) Line, $\overleftrightarrow{CD}$ (b) Line segment, $\overline{AB}$ (c) Ray, $\overrightarrow{FE}$
Step-by-step solution
1. Understand the definitions:
- A line extends infinitely in both directions. It is represented by a straight path with arrows on both ends.
- A ray has one endpoint and extends infinitely in one direction. It is represented by a straight path with an endpoint on one side and an arrow on the other.
- A line segment has two endpoints and a finite length. It is represented by a straight path with a point on each end.
2. Analyze figure (a):
The figure has points C and D. It has an arrow on the right side, indicating it extends infinitely in that direction, and it has an arrow on the left side, indicating it extends infinitely in that direction. Therefore, it is a line.
The name of the line can be written using its two points, such as $\overleftrightarrow{CD}$.
3. Analyze figure (b):
The figure has points A and B. It has a point on each end, indicating it is a finite segment with two endpoints. Therefore, it is a line segment.
The name of the line segment can be written using its two endpoints, such as $\overline{AB}$.
4. Analyze figure (c):
The figure has points E and F. It has an arrow on the left side, indicating it extends infinitely in that direction, and it has a point on the right side (F), indicating it is an endpoint. Therefore, it is a ray.
The name of the ray starts with the endpoint and then another point on the ray, such as $\overrightarrow{FE}$. Note that the order of points matters for rays; the first point is the endpoint.