**2D and 3D Shapes and Their Properties**

In geometry, shapes are classified into two main categories: 2D (two-dimensional) and 3D (three-dimensional) shapes. Each type of shape has its own unique properties and characteristics.

**2D Shapes**

### Definition

A 2D shape is a flat shape that can be drawn on a piece of paper or a flat surface. It has only two dimensions: length and width.

### Types of 2D Shapes

**Points**: A point is a location in space, represented by a single coordinate.**Lines**: A line is a set of points that extend infinitely in two directions.**Rays**: A ray is a line that extends from a single point to infinity in one direction.**Angles**: An angle is formed by two rays sharing a common endpoint.**Triangles**: A triangle is a polygon with three sides and three vertices.**Quadrilaterals**: A quadrilateral is a polygon with four sides and four vertices.**Polygons**: A polygon is a shape with at least three sides and three vertices.**Circles**: A circle is a set of points equidistant from a central point.

### Properties of 2D Shapes

**Angles**: The sum of interior angles of a polygon is always equal to 180°(n-2), where n is the number of sides.**Perimeter**: The perimeter of a polygon is the sum of the lengths of all its sides.**Area**: The area of a polygon is the amount of space inside the shape.

**3D Shapes**

### Definition

A 3D shape is a shape that has three dimensions: length, width, and height. It occupies space and can be seen from different angles.

### Types of 3D Shapes

**Prisms**: A prism is a polyhedron with two identical faces that are parallel to each other.**Pyramids**: A pyramid is a polyhedron with a single base and four triangular faces that meet at the apex.**Spheres**: A sphere is a set of points equidistant from a central point in three-dimensional space.**Cylinders**: A cylinder is a shape with two parallel and circular bases connected by a curved surface.**Cones**: A cone is a shape with a circular base and a curved surface that tapers to a point.

### Properties of 3D Shapes

**Surface Area**: The surface area of a 3D shape is the sum of the areas of all its faces.**Volume**: The volume of a 3D shape is the amount of space inside the shape.**Edges**: The edges of a 3D shape are the lines where two faces meet.

### Real-World Applications

Understanding 2D and 3D shapes and their properties is essential in various real-world applications, such as:

**Architecture**: Designing buildings, bridges, and other structures requires knowledge of 2D and 3D shapes.**Engineering**: Understanding shapes is crucial in designing machines, mechanisms, and other devices.**Art**: Artists use shapes to create compositions, sculptures, and other forms of art.**Science**: Shapes are used to describe the structure of molecules, cells, and other scientific concepts.

In conclusion, 2D and 3D shapes are fundamental concepts in geometry, and understanding their properties is essential in various aspects of our lives.