Geometry Basics

Study Notes

Points, Lines, and Planes
- A point has no size, only location
- A line extends infinitely in two directions
- A plane is a flat surface that extends infinitely
Angles and Measurements
- Angle: formed by two rays sharing a common endpoint
- Angle types: acute, right, obtuse, straight, reflex
- Measuring angles: degrees, radians
Properties of Shapes
- Congruent: same size and shape
- Similar: same shape, different size
- Symmetry: line or point of reflection
Triangles
- Types: equilateral, isosceles, scalene
- Angles: sum of interior angles = 180°
- Pythagorean theorem: a^2 + b^2 = c^2 (right triangles)
Circles
- Center: fixed point equidistant from all points on the circle
- Radius: distance from center to any point on the circle
- Circumference: distance around the circle
- Pi (π): constant ratio of circumference to diameter

Variables and Expressions
- Variables: letters or symbols representing unknown values
- Expressions: combinations of variables and numbers
- Simplifying expressions: combining like terms
Equations and Inequalities
- Equation: statement with equal signs (=)
- Inequality: statement with greater than (>), less than (<), or equal to (=)
- Solving equations: finding the value of the variable
Linear Equations
- Slope-intercept form: y = mx + b
- Point-slope form: y - y1 = m(x - x1)
- Graphing linear equations: straight lines
Quadratic Equations
- Standard form: ax^2 + bx + c = 0
- Factoring: breaking down into product of binomials
- Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Functions
- Domain: input values
- Range: output values
- Function notation: f(x) = output value

Points
- Have no size, only location
Lines
- Extend infinitely in two directions
Planes
- Are flat surfaces that extend infinitely
Angles
- Formed by two rays sharing a common endpoint
- Can be acute, right, obtuse, straight, or reflex
- Measured in degrees or radians
Properties of Shapes
- Congruent shapes are the same size and shape
- Similar shapes are the same shape, but different sizes
- Symmetry is a line or point of reflection
Triangles
- Can be equilateral, isosceles, or scalene
- The sum of interior angles is 180°
- The Pythagorean theorem is a^2 + b^2 = c^2 (for right triangles)
Circles
- Have a fixed center point equidistant from all points on the circle
- Have a radius, which is the distance from the center to any point on the circle
- Have a circumference, which is the distance around the circle
- Pi (π) is the constant ratio of circumference to diameter

Variables and Expressions
- Variables are letters or symbols representing unknown values
- Expressions are combinations of variables and numbers
- Expressions can be simplified by combining like terms
Equations and Inequalities
- Equations are statements with equal signs (=)
- Inequalities are statements with greater than (>), less than (<), or other comparison operators