Which pair of undefined terms is used to define the term parallel lines?
Point and line. Parallel lines are defined using the undefined terms point and line: two lines (each made up of points) that lie in the same plane and never intersect, no matter how far they are extended.
The answer
The pair of undefined terms used to define parallel lines is point and line. In geometry, parallel lines are two lines in the same plane that never meet — and since a line is itself built from points, the definition rests on the undefined terms point and line.
Geometry begins with three undefined terms: point, line, and plane. They are called "undefined" not because we do not understand them, but because they are the starting vocabulary — the most basic ideas that cannot be built from anything simpler. Every other geometric term (segment, ray, angle, parallel lines) is defined using these building blocks.
A point marks a location with no size. A line is a straight, one-dimensional path of points extending forever in both directions. Using just these two ideas, we say two lines are parallel when they are coplanar and share no common point.
Why the other options are wrong
- Point and plane — a plane is needed as background context (parallel lines must be coplanar), but the definition is stated in terms of the lines themselves and the points they share. The core pair naming what parallel lines are is point and line, not point and plane.
- Line and plane — this pair leaves out the point, yet the crucial condition (the lines never share a point) depends on points. Without "point," you cannot state the non-intersection requirement.
- Line and angle or any option including angle — angle is a defined term, not an undefined one. Since the question asks specifically for a pair of undefined terms, anything involving angle, segment, or ray is automatically wrong.
The bigger picture
The subtle point students miss is that parallel lines are usually described as coplanar, so a plane hovers in the background. But "undefined terms used to define" asks which basic terms the definition is constructed from. Two lines are parallel precisely when they contain no common point — so line provides the objects and point provides the test for intersection.
Contrast this with perpendicular lines, which also use point and line but add the defined term "right angle" to specify how they meet. And skew lines — lines that never meet but are not coplanar — show why the plane matters conceptually even when it is not the named defining pair. Mastering the three undefined terms makes every later definition in geometry click into place.
Which pair of undefined terms is used to define the term parallel lines?
Frequently asked
What are the three undefined terms in geometry?
The three undefined terms are point, line, and plane. They are the most basic ideas in geometry and cannot be built from simpler terms, so every other term — segment, ray, angle, parallel lines — is defined using them.
Why are point, line, and plane called undefined terms?
They are called undefined because they are the starting vocabulary of geometry. There is nothing more basic to define them with, so they are described intuitively (a location, a straight path, a flat surface) and accepted as the foundation for all other definitions.
What undefined terms define perpendicular lines?
Perpendicular lines also rely on the undefined terms point and line, but their definition adds the defined term "right angle": two lines that intersect at a point to form a 90-degree angle.
How are parallel lines formally defined?
Parallel lines are two lines in the same plane that never intersect, no matter how far they are extended — equivalently, coplanar lines that share no common point. The definition is built from the undefined terms point and line.