Geometry Basics

Study Notes

A point is a location in space, represented by a set of coordinates (x, y, z)
A line is a set of points extending infinitely in two directions
A plane is a flat surface that extends infinitely in all directions

An angle is formed by two rays sharing a common endpoint (vertex)
Types of angles:
1. Acute angle: less than 90 degrees
2. Right angle: exactly 90 degrees
3. Obtuse angle: greater than 90 degrees but less than 180 degrees
4. Straight angle: exactly 180 degrees
Measurement units:
- Degrees (°): used to measure angles
- Units of length (e.g. meters, feet): used to measure distances and lengths

Types of shapes:
1. 2D shapes: flat shapes with length and width (e.g. triangles, quadrilaterals, polygons)
2. 3D shapes: solid shapes with length, width, and height (e.g. pyramids, prisms, spheres)
Properties of 2D shapes:
- Number of sides
- Number of angles
- Types of angles (e.g. acute, right, obtuse)
- Sum of interior angles (e.g. 180° for triangles, 360° for quadrilaterals)
Properties of 3D shapes:
- Number of faces
- Number of edges
- Number of vertices
- Volume (e.g. cubic units)

Theorems:
- Pythagorean theorem: a^2 + b^2 = c^2 (for right triangles)
- Angle sum theorem: sum of interior angles of a polygon = (n-2) × 180°
Formulas:
- Perimeter of a polygon: P = n × side length
- Area of a triangle: A = (base × height) / 2
- Volume of a rectangular prism: V = length × width × height

An angle is formed by two rays sharing a common endpoint (vertex).
Angles can be classified into four types: acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), and straight (exactly 180 degrees).
Degrees (°) are used to measure angles, while units of length (e.g. meters, feet) are used to measure distances and lengths.

Shapes can be classified into two categories: 2D shapes (flat shapes with length and width) and 3D shapes (solid shapes with length, width, and height).
2D shapes have properties such as number of sides, number of angles, types of angles, and sum of interior angles.
3D shapes have properties such as number of faces, number of edges, number of vertices, and volume.

The Pythagorean theorem states that a^2 + b^2 = c^2 for right triangles.
The angle sum theorem states that the sum of interior angles of a polygon is (n-2) × 180°.
Formulas for finding perimeter, area, and volume of different shapes include: P = n × side length for perimeter of a polygon, A = (base × height) / 2 for area of a triangle, and V = length × width × height for volume of a rectangular prism.