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Standard G.RL.1.1

Geometry's Building Blocks

Understanding the basics: Undefined Terms, Definitions, Postulates, and Theorems.

Why Bother with This Stuff?

Think of geometry like building with LEGOs. You need basic bricks (undefined terms), instructions on how specific pieces work (definitions), fundamental rules for how bricks connect (postulates), and cool structures you can prove you can build (theorems).

Getting these basics down helps you understand *why* things work in geometry and how to build logical arguments (proofs later on!). Let's break them down.

1. Undefined Terms: The Starting Point

These are the most basic ideas in geometry. We don't formally define them, but we all have an intuitive idea of what they mean. They're the absolute foundation.

Point

(Click me!)

A specific location with no size. Represented by a capital letter (e.g., Point A).

Line

(Click me!)

A straight path extending forever in both directions. Has length, no width. Named $\overleftrightarrow{AB}$ or line $m$.

Plane

(Click me!)

A flat surface extending forever. Has length and width, no thickness. Named Plane ABC or $\mathcal{P}$.

2. Definitions: Giving Names to Ideas

Definitions use undefined terms or previously defined terms to give precise meanings to other geometric concepts.

Line Segment

Part of a line with two endpoints and all points between. Named $\overline{AB}$.

Ray

Part of a line with one endpoint, extending forever in one direction. Named $\overrightarrow{AB}$ (starts at A).

Angle

Formed by two rays sharing a common endpoint (vertex). Measured in degrees. Named $\angle ABC$ (B is vertex).

Parallel Lines

Two lines in the same plane that never intersect.

Collinear Points

Points that lie on the same line.

Coplanar Points

Points that lie on the same plane.

3. Postulates (or Axioms): Rules We Accept

Postulates are statements we accept as true *without proof*. They are fundamental assumptions.

4. Theorems: Truths We Can Prove

Theorems are statements proven true using undefined terms, definitions, postulates, etc.

Vertical Angles Theorem:

If two lines intersect, then vertical angles are congruent (equal measure).

Corresponding Angles Theorem:

If two parallel lines are cut by a transversal, then corresponding angles are congruent.

These require proof, unlike postulates!

Let's Match!

Click a term on the left, then click its matching description on the right. Good luck!

Undefined Term
Definition
Postulate
Theorem
A statement accepted as true without proof (e.g., Through 2 points is 1 line).
A basic idea not formally defined (e.g., Point, Line, Plane).
A statement that can be proven true (e.g., Vertical angles are congruent).
Gives precise meaning using undefined or defined terms (e.g., definition of a line segment).

Quick Check: Test Your Knowledge!

1. Which is an UNDEFINED term?

2. A statement accepted true WITHOUT proof:

3. "Vertical angles are congruent" is a:

4. Which describes part of a line with two endpoints?

5. "Through any two points, there is exactly one line." This is a: