Three words you never get to define
Point, line, and plane are undefined. You describe them. You do not prove them. Every other word in this module is built out of those three.
- A point is a location. No size, no dimension. Named with a capital letter: point A.
- A line is a stream of points that goes forever in two directions. One dimension: length. Named with two points (line AD) or a lowercase script letter (line m).
- A plane is a flat surface that goes forever in two dimensions. Named with three noncollinear points (plane EFG) or a script capital (plane P).
Collinear points sit on the same line. Coplanar points sit in the same plane. Non- just means they do not.
Break it down for me
Think of them as ingredients you are allowed to use without a recipe. You cannot measure a true line (it never ends), so a formal definition would fail. Geometry still needs a starting place, so it names the three ingredients and moves on.
Say out loud: a point has how many dimensions? A line? A plane? Peek: 0, 1, 2.
The ones you can define
A defined term uses an undefined term in its definition. That one idea is a live quiz item.
- A line segment is a piece of a line with two endpoints. Named AB or BA, with a bar on top.
- A ray has one endpoint and goes forever in one direction. Named with the endpoint first: ray AB is not ray BA.
- An angle is two noncollinear rays that share an endpoint, the vertex. Named ∠B, ∠ABC, or ∠CBA. The vertex stays in the middle.
The two rays of an angle meet in exactly one point. That point is the vertex.
Parallel, perpendicular, circle
Parallel lines lie in the same plane and never meet. Written a ∥ b. Same-direction arrows on the drawing mark them.
Perpendicular lines meet at 90°. Written c ⊥ d. A little square in the corner is the 90° mark. All four corners at that crossing are right angles, so they are congruent.
A circle is the set of all points in a plane that are the same distance from a center. Named ⊙P if P is the center. That distance is the radius. “All points the same distance from a center” is almost right. The missing words are in a plane.
Accepted vs proven
A postulate is accepted as fact. Nobody has to prove it in this course. Example: through any two points there is exactly one line.
A theorem looks true and still has to be proven from postulates, definitions, and undefined terms. Pythagorean theorem is the famous one. Vertical angles are congruent is one you will prove in 01.07.
A conjecture is a guess from a pattern. “Every rectangle I drew had opposite sides equal, so maybe all of them do.” Useful. Not a fact yet.
If a stem says “If two distinct planes intersect, then their intersection is a line,” the geometry word for that sentence is postulate. It is not a definition of the word plane, and it is not a theorem you prove in 01.01.
Break it down for me
Dashboard of a jet: the altimeter reading is treated as true so you can fly. That is a postulate. “We will clear that ridge” is a claim you still check with other instruments. That is a theorem.
Say out loud: do you prove a postulate? Peek: no.
Four postulates to keep
- Points: through any two points, exactly one line.
- Intersecting lines: two lines meet in exactly one point. If they met in two, they would be the same line.
- Intersecting planes: two distinct planes meet in exactly one line. Picture two walls and the corner between them.
- Coplanar points: through any three noncollinear points, exactly one plane. A fourth point can sit off that plane.
The shortest path between two points is that unique line. That is why the first postulate shows up in distance talk later.
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.