Question

Three undefined terms in mathematics:

I. Point

II. Line

III. Plane

The mathematical term parallel lines explicitly uses the undefined term(s)
.

The mathematical term perpendicular lines explicitly uses the undefined term(s)
.

The mathematical term line segment explicitly uses the undefined term(s)
.

Answer 1

In mathematics, the terms "point," "line," and "plane" are considered undefined because they form the foundational concepts from which other geometric ideas are developed. Here's how the undefined terms are used in the specified mathematical terms:

1. The mathematical term **parallel lines** explicitly uses the undefined term(s) **line** (since parallel lines are defined as lines that do not intersect).

2. The mathematical term **perpendicular lines** explicitly uses the undefined term(s) **line** (as perpendicular lines are defined as lines that intersect at a right angle).

3. The mathematical term **line segment** explicitly uses the undefined term(s) **line** (since a line segment is a part of a line that is bounded by two distinct endpoints).

In summary:
- **Parallel lines** use the undefined term **line**.
- **Perpendicular lines** use the undefined term **line**.
- **Line segment** uses the undefined term **line**.