From the line to the dodecahedron
Geometry begins with points and lines and never really stops. The same handful of properties — sides, angles, symmetry — describe everything from a triangle to a sphere.
The basics
A point has no size. A line stretches forever in two directions. A line segment stops at endpoints. A ray stops at one end and continues forever the other way.
Angles
Acute < 90°, right = 90°, obtuse between 90° and 180°, straight = 180°, reflex > 180°.
Polygons
A closed figure with straight sides. Named by side count: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), heptagon (7), octagon (8). A regular polygon has equal sides and equal angles.
Solids
3D shapes: cube, prism, pyramid, cylinder, cone, sphere, torus. Polyhedra have flat polygon faces. The five Platonic solids are the only regular convex polyhedra.
Headline formulas
Hands-on tools
Click a shape, build a polygon, or count faces on a solid.
Shape gallery
Click any shape to see its properties.
Regular polygon builder
Slide to change the side count from 3 (triangle) to 20 (icosagon).
3D solid explorer
Pick a solid — see faces, edges and vertices, plus a wireframe sketch.
Lines of symmetry
A regular polygon with n sides has exactly n lines of symmetry.
A regular pentagon has 5 lines of symmetry, each through a vertex and the midpoint of the opposite side.
Quiz
Flashcards
Tap a card to flip. ← / → keys to navigate.
Daily challenge
A new problem every day. Same problem for everyone, worldwide. Build a streak — one shot per day.
For teachers
Print-ready worksheet, answer key, teaching tips and standards alignment.
Teaching tips
Standards alignment
Reference
Formula sheet plus Wikipedia photos.
Formula sheet
Photo gallery
Images sourced from Wikipedia.