Geometry Basics

Definition: Study of shapes, sizes, and properties of space.
Basic Concepts:
- Point: An exact location in space, no dimensions.
- Line: A straight one-dimensional figure with length, extending infinitely in both directions.
- Plane: A flat two-dimensional surface extending infinitely.
Types of Angles:
- Acute: Less than 90 degrees
- Right: Exactly 90 degrees
- Obtuse: Greater than 90 degrees but less than 180 degrees
- Straight: Exactly 180 degrees
Shapes:
- Triangles: Sum of angles = 180 degrees.
  - Types: Equilateral, Isosceles, Scalene.
- Quadrilaterals: Sum of angles = 360 degrees.
  - Types: Square, Rectangle, Parallelogram, Trapezoid.
- Circles: Defined by radius, diameter, and circumference.
  - Area = πr², Circumference = 2πr.
Theorems:
- Pythagorean Theorem: In a right triangle, a² + b² = c².
- Congruence: Two shapes are congruent if they have the same size and shape.

Definition: Branch of mathematics dealing with symbols and rules for manipulating those symbols.
Basic Concepts:
- Variables: Symbols that represent unknown values (e.g., x, y).
- Expressions: Combinations of variables, numbers, and operations (e.g., 3x + 2).
- Equations: Statements of equality (e.g., 2x + 3 = 7).
Operations:
- Addition, Subtraction, Multiplication, and Division: Fundamental arithmetic operations applied to algebraic expressions.
Solving Equations:
- Linear Equations: In the form ax + b = c.
- Quadratic Equations: In the form ax² + bx + c = 0; solutions found using factoring, completing the square, or the quadratic formula.
Functions:
- Definition: A relation between a set of inputs and a set of possible outputs, often expressed as f(x).
- Types:
  - Linear Functions: f(x) = mx + b; graph is a straight line.
  - Quadratic Functions: f(x) = ax² + bx + c; graph is a parabola.
Inequalities:
- Represent a range of values rather than a single value (e.g., x > 5).
- Can be solved similarly to equations, but the direction of the inequality can change when multiplying/dividing by a negative number.
Polynomials:
- Expressions involving variables raised to whole number powers (e.g., 2x³ + 3x² - x + 5).
- Can be added, subtracted, multiplied, and divided.

Definition: Study of shapes, sizes, and properties of space.
Basic Concepts:
- Point: A specific location with no dimensions.
- Line: Straight, one-dimensional figure extending infinitely in both directions.
- Plane: Flat, two-dimensional surface extending infinitely.
Types of Angles:
- Acute: Less than 90 degrees.
- Right: Exactly 90 degrees.
- Obtuse: Greater than 90 degrees but less than 180 degrees.
- Straight: Exactly 180 degrees.
Shapes:
- Triangles:
  - Sum of angles = 180 degrees.
  - Types:
    - Equilateral: All sides equal.
    - Isosceles: Two sides equal.
    - Scalene: All sides different.
- Quadrilaterals:
  - Sum of angles = 360 degrees.
  - Types:
    - Square: All sides equal, all angles right.
    - Rectangle: Opposite sides equal, all angles right.
    - Parallelogram: Opposite sides and angles equal.
    - Trapezoid: One pair of parallel sides.
- Circles:
  - Defined by radius, diameter, and circumference.
  - Area = πr², Circumference = 2πr.
Theorems:
- Pythagorean Theorem: In a right triangle, a² + b² = c², where c is the hypotenuse.
- Congruence: Two shapes are congruent if they have the same size and shape.

Definition: Branch of mathematics dealing with symbols and rules for manipulating those symbols.
Basic Concepts:
- Variables: Symbols representing unknown values.
- Expressions: Combination of variables, numbers, and operations.
- Equations: Statements of equality.
- Operations: Addition, subtraction, multiplication, and division are applied to algebraic expressions.
Solving Equations:
- Linear Equations: In the form ax + b = c.
- Quadratic Equations: In the form ax² + bx + c = 0; solutions found using factoring, completing the square, or the quadratic formula.
Functions:
- Definition: A relation between a set of inputs and a set of outputs.
- Types:
  - Linear Functions: f(x) = mx + b; graph is a straight line.
  - Quadratic Functions: f(x) = ax² + bx + c; graph is a parabola.
Inequalities:
- Represent a range of values rather than a single value.
- Can be solved similarly to equations, but flipping the inequality sign is necessary when multiplying or dividing by a negative number.
Polynomials:
- Expressions involving variables raised to whole number powers.
- Can be added, subtracted, multiplied, and divided.