Every shape, angle, and measurement in geometry is built from just a few simple ideas. Once you know points, lines, rays, segments, and planes, you're ready for everything else.
Geometry starts with a few basic ideas that are so simple, they're never really "defined" — just described. Everything else in geometry is built out of these.
A point is an exact location in space. It has no size — no length, width, or height — just a position. We draw it as a small dot and name it with a capital letter.
A line is a straight path that goes on forever in both directions. It has no thickness. Any two points on the line are enough to name it — the arrows in the notation show that it never ends.
🗣️ Say it out loud: "line AB" — since a line goes both directions forever, it doesn't matter which point you say first. Line AB and line BA are the same line.
A ray has one endpoint and goes on forever in only one direction. Think of a flashlight beam — it starts at a fixed point and shines outward without stopping. The endpoint is always named first.
🗣️ Say it out loud: "ray AB" — and order matters here! Ray AB starts at A and shoots through B and beyond. Ray BA is a completely different ray — it starts at B and shoots the opposite way, through A and beyond.
A segment is the part of a line between two endpoints — no arrows, because it stops on both sides. This is the one you'll measure most often, since it has a definite length.
🗣️ Say it out loud: "segment AB" — just like a line, order doesn't matter. Segment AB and segment BA name the exact same segment.
Notice how the SAME two letters can mean three different things depending on the symbol above them: a line, a ray, or a segment. Always check the notation, not just the letters! Here's a quick reference for reading each one:
• Arrows on both ends → "line AB" — order doesn't matter
• An arrow on one end only → "ray AB" — order matters! The first letter is always the endpoint
• No arrows → "segment AB" — order doesn't matter
A plane is a perfectly flat surface that extends forever in every direction — imagine an endless, paper-thin sheet with no edges. A plane has length and width, but no thickness.
A plane can be named with a single capital letter, or by naming any three points on it that aren't all on the same line (like P, Q, and R here) — those three points pin down exactly one flat surface.
A sheet of paper, a tabletop, or a wall are all real-world stand-ins for a plane — except a real plane has no edges and goes on forever, and it's perfectly flat with zero thickness.
Once you have points, lines, and planes, geometry is really about how they relate to each other. Here are five relationships worth knowing:
Points that lie on the same line are called collinear. A and B and C here are all collinear — you could draw one straight line through all three.
Points or lines that lie in the same plane are called coplanar. Any three points are always coplanar — it's only once you add a fourth point that it might not fit in that same flat surface.
Two lines that cross at exactly one point are intersecting lines. That shared point (P here) is the only spot the two lines have in common.
Lines in the same plane that never intersect, no matter how far you extend them, are parallel. They stay exactly the same distance apart the whole way. The matching tick marks show they're parallel.
Lines that intersect to form a right angle (90°) are perpendicular. The small corner mark at the intersection — like the corner of a square — is the standard symbol for a right angle.
Test what you've learned with these two quick checks.
Look at the diagram, then pick the correct term.
Look at the diagram, then pick the correct relationship.