Classification of Polygons and 2D Shapes

Definition: A polygon is a closed figure with straight sides.
Types of Polygons:
1. Regular Polygons: All sides and angles are equal (e.g., equilateral triangle, square).
2. Irregular Polygons: Sides and angles are not equal (e.g., trapezium).
Based on Number of Sides:
1. Triangle: 3 sides
2. Quadrilateral: 4 sides
3. Pentagon: 5 sides
4. Hexagon: 6 sides
5. Heptagon: 7 sides
6. Octagon: 8 sides
7. Nonagon: 9 sides
8. Decagon: 10 sides
Convex vs. Concave:
- Convex: All interior angles are less than 180°.
- Concave: At least one interior angle is greater than 180°.

General Properties:
- Closed figure: All sides connect to form a boundary.
- Dimensions: Defined by length and width (no depth).
Triangles:
- Sum of interior angles = 180°
- Types: Equilateral, Isosceles, Scalene based on side lengths; Acute, Right, Obtuse based on angle sizes.
Quadrilaterals:
- Sum of interior angles = 360°
- Types: Square, Rectangle, Rhombus, Parallelogram, Trapezium.
- Opposite sides of parallelograms are equal and parallel.
Circles:
- Defined by a center point and radius.
- Circumference = 2πr; Area = πr².
Symmetry:
- Reflection Symmetry: Shape is identical on both sides of a line.
- Rotational Symmetry: Shape looks the same after a certain degree of rotation.
Perimeter and Area:
- Perimeter: Total distance around the shape.
- Area: Measure of space within the shape (varies by shape).
Vertices and Edges:
- Vertices: Points where two sides meet.
- Edges: Line segments that form the sides of the shape.

A polygon is defined as a closed figure composed of straight sides.
Regular Polygons have all sides and angles equal, such as equilateral triangles and squares.
Irregular Polygons have unequal sides and angles, like trapeziums.
Polygons can be classified by the number of sides:
- Triangle: 3 sides.
- Quadrilateral: 4 sides.
- Pentagon: 5 sides.
- Hexagon: 6 sides.
- Heptagon: 7 sides.
- Octagon: 8 sides.
- Nonagon: 9 sides.
- Decagon: 10 sides.

General Properties: 2D shapes are closed figures where all sides connect to form a boundary, defined by length and width without depth.
Triangles:
- Interior angles sum to 180°.
- Type categories include Equilateral, Isosceles, Scalene (based on side lengths) and Acute, Right, Obtuse (based on angle sizes).
Quadrilaterals:
- Sum of interior angles equals 360°.
- Types include Square, Rectangle, Rhombus, Parallelogram, and Trapezium.
- Parallelograms feature equal and parallel opposite sides.
Circles:
- Defined by a center point and radius.
- Circumference is calculated by 2πr, and area by πr².
Symmetry:
- Reflection Symmetry occurs when the shape is identical on either side of a line.
- Rotational Symmetry exists if the shape appears the same after being rotated by a certain angle.
Perimeter and Area:
- Perimeter represents the total distance around a shape, while area measures the space within the shape and varies based on the shape type.
Vertices and Edges:
- Vertices are points where two sides intersect.
- Edges are the line segments that make up the sides of shapes.

Definition:
- Symmetry involves a balanced arrangement of parts on either side of a dividing line or around a central point.

Line Symmetry (Reflective Symmetry):
- Achieved when a shape can be divided into two identical halves by a straight line.
- Example includes butterflies and isosceles triangles, each having one line of symmetry.
Rotational Symmetry:
- Present when a shape maintains its appearance after being rotated around a central point at specific angles.
- Stars and squares exhibit this type of symmetry, with squares showing symmetry at every 90° interval.
Point Symmetry:
- Occurs when every part of the shape has a counterpart at an equal distance from a central point, but in the opposite direction.
- The letter "S" and certain circular designs are examples.

Line Symmetry:
- Count the number of lines of symmetry present in the shape.
- Techniques such as mirroring or folding can help test for equal halves.
Rotational Symmetry:
- Determine the order of symmetry by assessing how many times a shape aligns with its original position in a full 360° rotation.
Point Symmetry:
- Check if each part of the shape has a corresponding counterpart at equal distance from the central point.

Enhances aesthetic appeal in various forms of art and design.
Fundamental in natural phenomena, observable in structures like leaves and flowers.
Utilized in architecture and engineering for balanced and appealing designs.

Circle: Infinite lines of symmetry; possesses rotational symmetry at every angle.
Square: 4 lines of symmetry; 4-fold rotational symmetry.
Rectangle: 2 lines of symmetry; 2-fold rotational symmetry.
Equilateral Triangle: 3 lines of symmetry; 3-fold rotational symmetry.
Pentagon: 5 lines of symmetry (in a regular pentagon); 5-fold rotational symmetry.