Geometric Shapes and Figures

How shapes are classified, and why the definitions matter.

Geometry classifies figures by properties that stay true no matter how the figure is moved, turned or scaled. A definition names the smallest set of properties that pins a shape down.

Polygons

A polygon is a closed plane figure made of straight segments. It is regular when all sides and all angles are equal. Interior angles of any polygon with n sides sum to (n − 2) × 180°, so a triangle gives 180° and a quadrilateral 360°.

Classification is nested

Every square is a rectangle, every rectangle is a parallelogram, and every parallelogram is a quadrilateral. The nesting runs one way only. Students who read these as separate boxes rather than as levels get inclusion questions wrong.

Solids

Prisms and cylinders have two congruent parallel bases and constant cross-section, so volume is base area times height. Pyramids and cones taper to a point and hold exactly one third the volume of the prism or cylinder on the same base.