01.01 Basics of Geometry

Module 01 — Geometry Foundations

The big idea Three words start geometry: point, line, and plane. Defined terms build from them; postulates are accepted, while theorems must be proven.

By the end you can

  • Tell undefined terms from defined terms.
  • Recognize lines, rays, segments, parallel lines, and perpendicular lines from their markings.
  • Tell a postulate from a theorem or conjecture.

Three words you never define

Point, line, and plane are undefined. You describe them; you do not build their definitions from earlier geometry words. Every other word in this module starts with these three.

  • A point is a location with no size or dimension. Name it with a capital letter.
  • A line is a stream of points that goes forever in two directions. It has one dimension: length.
  • A plane is a flat surface that goes forever in two dimensions.

Three words you never define (2)

Collinear points sit on one line. Coplanar points sit in one plane. The prefix non- means they do not.

Quiz trap: a plane has length and width and is undefined. It does not have endpoints; endpoints belong to segments.

The terms you can define

A defined term uses an undefined term in its definition.

  • A line segment is a piece of a line with two endpoints.
  • A ray has one endpoint and continues forever in one direction. Name the endpoint first: ray AB is not ray BA.
  • An angle is two noncollinear rays sharing one endpoint, the vertex. In ∠ABC, the vertex B stays in the middle.

The two rays of an angle meet in exactly one point: the vertex.

The terms you can define (2)

segmentrayline: arrows both ways
Lookalike trio: segment = two endpoints. Ray = one endpoint and one arrow. Line = two arrows and no endpoints.

Parallel, perpendicular, circle

Parallel lines lie in the same plane and never meet, written a ∥ b. Matching arrow marks identify them.

Perpendicular lines meet at 90°, written c ⊥ d. A little square marks the right angle.

A circle is the set of all points in a plane that are the same distance from a center. That distance is the radius.

Parallel, perpendicular, circle (2)

a ∥ bc ⊥ d
Defined from undefined: parallel lines use line and plane. Coplanar is a defined word, so it can be a decoy.

Accepted versus proven

A postulate is accepted as fact. A theorem must be proven from postulates, definitions, and earlier results. A conjecture is a pattern-based guess that has not been proven.

“Through any two points there is exactly one line” is a postulate. “Vertical angles are congruent” is a theorem you will prove in 01.07.

Accepted versus proven (2)

If a stem says, “If two distinct planes intersect, then their intersection is a line,” the geometry word for that statement is postulate. It is not a definition of plane and not a theorem you prove here.

Four postulates to keep

  1. Through any two points, there is exactly one line.
  2. Two distinct intersecting lines meet in exactly one point.
  3. Two distinct intersecting planes meet in exactly one line.
  4. Through any three noncollinear points, there is exactly one plane.

These are starting facts. You use them; you do not prove them in this lesson.

Name this figure

Quizzes flash a picture and ask line, ray, segment, or point. Tap the name. The picture changes after each one.

Practice like 01.01

Ten questions. Mix of LC (short definition) and MC (which statement is true, or is this picture a ray). New items. Not the Canvas quiz.

1 / 10 0 correct