Standard G.RL.1.1
Understanding the basics: Undefined Terms, Definitions, Postulates, and Theorems.
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.
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.
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A specific location with no size. Represented by a capital letter (e.g., Point A).
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A straight path extending forever in both directions. Has length, no width. Named $\overleftrightarrow{AB}$ or line $m$.
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A flat surface extending forever. Has length and width, no thickness. Named Plane ABC or $\mathcal{P}$.
Definitions use undefined terms or previously defined terms to give precise meanings to other geometric concepts.
Part of a line with two endpoints and all points between. Named $\overline{AB}$.
Part of a line with one endpoint, extending forever in one direction. Named $\overrightarrow{AB}$ (starts at A).
Formed by two rays sharing a common endpoint (vertex). Measured in degrees. Named $\angle ABC$ (B is vertex).
Two lines in the same plane that never intersect.
Points that lie on the same line.
Points that lie on the same plane.
Postulates are statements we accept as true *without proof*. They are fundamental assumptions.
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!
Click a term on the left, then click its matching description on the right. Good luck!