Geometry 101: Basic Terms and Concepts

Undefined Terms

• Point

  • Represented as a dot in geometry.
  • Infinitesimally small, used to locate a position in space.
  • Notated with a capital letter (e.g., Point A, Point B).
  • Zero dimensional (0D).

• Line

  • Extends infinitely in both directions, a set of points.
  • Identified using two points on the line (e.g., XY or YX) with a line symbol above the letters.
  • One dimensional (1D).

• Plane

  • A flat surface extending infinitely, like a floor or ceiling.
  • Represented as a rectangle or parallelogram.
  • Labeled using a capital letter or three non-collinear points (e.g., Plane M or Plane ABC).
  • Two dimensional (2D).
  • Three non-collinear points ensure only one plane passes through them.

• Space

  • Three dimensional (3D).

Segments, Rays, and Opposite Rays

• Segment

  • A portion of a line with two endpoints (e.g., Segment XY or YX with a bar above).

• Ray

  • A line that starts at an endpoint and extends infinitely in one direction.
  • Notated with an arrow pointing to the right above the letters (e.g., Ray CD).
  • Conventionally written with the arrow pointing right, even if direction varies.

• Opposite Rays

  • Two rays with the same starting point, extending in opposite directions.
  • Together, they form a line (e.g., Rays RT and RS).

Intersections

• Lines Intersection

  • Two lines intersect at a point unless they are parallel or skew.

• Planes Intersection

  • Two planes intersect at a line.

Example Questions and Notations

1. Naming a Point: Possible answers include Point T, S, or W.
2. Naming a Line: Example - Line WX with a line symbol above.
3. Naming a Segment: Example - Segment SX with a bar above.
4. Naming a Ray: Example - Ray XR with an arrow pointing right.
5. Pair of Opposite Rays: Example - Rays XS and XR.
6. Naming a Plane: Example - Plane A or Plane XSW.
7. Another Name for a Plane: Example - Plane XRW.
8. Collinear Points: Example - Points S, X, and R.
9. Coplanar Points: Example - Points T, W, and X.
10. Non-Collinear Point with Line WX: Example - Point T.
11. Non-Coplanar Point with Plane B: Example - Point R.
12. Intersection of Lines L and M: Occurs at Point X.
13. Intersection of Planes A and B: Occurs along Line M or Line XW.

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