Fundamentals of Geometry Terms

Sep 15, 2024

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Lecture Notes: Introduction to Geometry - Lesson 1.1

Key Concepts

Undefined Terms in Geometry

  • Undefined terms: Basic concepts not formally defined but universally agreed upon.
    • Points
    • Lines
    • Planes

Points

  • Represented by a dot.
  • Indicate locations in space.
  • Infinitely small, no actual size.
  • Named using a capital letter (e.g., Point A).

Lines

  • Straight paths extending in two opposite directions without end.
  • Composed of infinite points.
  • Naming lines:
    • Use two points on the line (e.g., Line BC or Line CB).
    • Use a lowercase letter (e.g., line l).

Planes

  • Flat, two-dimensional surfaces extending endlessly in all directions.
  • Composed of infinite points.
  • Naming planes:
    • Use three non-collinear points (e.g., Plane DEF).
    • Use a capital letter without a point (e.g., Plane G).

Related Concepts

Collinear and Coplanar Points

  • Collinear Points: Points on the same line.
  • Coplanar Points: Points on the same plane.

Examples and Practice

  • Naming lines: FG could also be named Line GF or Line b.
  • Naming planes: Use non-collinear points, e.g., Plane HJI or Plane GJI.
  • Identifying collinear points: Points H, G, I are collinear.
  • Identifying coplanar points: Points H, G, J, I are coplanar.

Additional Vocabulary

Line Segment

  • A part of a line with two endpoints.
  • Naming: Use endpoints (e.g., Segment AB or BA).

Ray

  • A part of a line with one endpoint, extending endlessly in one direction.
  • Initial point is crucial for naming (e.g., Ray CD).

Opposite Rays

  • Two rays with a common initial point extending in opposite directions.
  • Example: Ray EF and Ray EG.

More Examples

  • Naming segments: LM could also be ML.
  • Identifying rays: From point K, possible rays include KJ, KL, KM, KN.
  • Opposite rays: KJ & KN, KL & KM.

Intersections

Intersections of Lines and Planes

  • Line-Line Intersection: At a single point.
  • Line-Plane Intersection: At a single point with part of the line potentially hidden (dotted line).
  • Plane-Plane Intersection: Along a line, visible or hidden parts shown dotted.

That's it for this lesson on basic geometric structures and terms, focusing on naming and intersections.