Geometry - Classifying 2D and 3D Shapes

2D shapes (Polygons) are flat figures with three or more straight sides. Common polygons include triangles ($3$ sides), quadrilaterals ($4$ sides), pentagons ($5$ sides), hexagons ($6$ sides), and octagons ($8$ sides). Imagine a hexagon as a shape with $6$ corners and $6$ straight edges connecting them, like a cell in a honeycomb.

Triangles are classified by their sides and angles. An equilateral triangle has $3$ equal sides and $3$ equal angles of $60^{\circ}$. An isosceles triangle has at least $2$ equal sides. A scalene triangle has no equal sides. A right-angled triangle contains one $90^{\circ}$ angle, looking like the corner of a square.

Quadrilaterals are 4-sided shapes. A rectangle has $4$ right angles and opposite sides of equal length. A square is a special rectangle with $4$ equal sides. A parallelogram has two pairs of parallel sides, while a rhombus is a parallelogram with $4$ equal sides, often looking like a tilted diamond.

3D shapes are solid objects with three dimensions: length, width, and height. They are made of faces (flat surfaces), edges (lines where faces meet), and vertices (corners where edges meet). For example, a cube looks like a box where every face is an identical square.

Prisms and Pyramids are two main types of 3D shapes. A prism has two identical bases connected by rectangular faces, like a triangular prism which has two triangles at the ends. A pyramid has one base and triangular faces that meet at a single point called the apex, such as the Great Pyramids which have a square base.

Curved 3D shapes include spheres, cylinders, and cones. A sphere is perfectly round like a ball and has no edges or vertices. A cylinder has two circular bases and one curved surface (like a soda can). A cone has one circular base and one vertex at the top (like an ice cream cone).

Lines of Symmetry are imaginary lines where you can fold a shape so that both halves match exactly. A square has $4$ lines of symmetry (vertical, horizontal, and two diagonals), whereas an irregular shape might have no lines of symmetry at all.