Basic Concepts Summary

Geometry · Axiom Academy

SUMMARY Unit 1 Summary: Basic Geometric Concepts Everything geometry is built on — the undefined terms, how we name them, and the two coordinate formulas you'll use everywhere. Point , line , and plane are the undefined terms — we describe them, but never define them in terms of anything simpler. Everything else is built from them. A segment has two endpoints; a ray has one endpoint and goes on forever. For a ray the order of letters matters — . Notation carries meaning: a bar means a segment, an arrow means a ray or line, and no symbol (just AB ) means the length — a number. The midpoint of a segment is the average of the endpoints' coordinates; it splits the segment into two congruent halves. The distance formula is the Pythagorean theorem in disguise — it measures the length of a segment between two points. The Segment Addition Postulate , AB + BC = AC , lets you treat lengths along a line like pieces you can add and subtract. Core Concept Points, Lines & Planes The three undefined terms . A point is a location with no size; a line is straight and extends forever in both directions; a plane is a flat surface extending forever. We accept them without definition and build everything else on top. Key idea: "undefined" doesn't mean unknown — it means foundational. Watch out for: a line and a plane have no thickness, even though our drawings do.

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