Geometry Basics: Points, Lines, and Planes

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 in all directions
Angles and Measurements:
- Angle: formed by two rays sharing a common endpoint
- Types of angles: acute, obtuse, right, straight, reflex
- Measurement units: degrees, radians, minutes, seconds
Properties of Shapes:
- Congruent figures: same size and shape
- Similar figures: same shape, but not necessarily same size
- Symmetry: line, rotational, or point symmetry
Perimeter and Area:
- Perimeter: distance around a shape
- Area: size of a shape's interior
- Formulas for calculating perimeter and area of various shapes (e.g., triangles, quadrilaterals, circles)

Number Systems:
- Natural numbers: 1, 2, 3, ...
- Whole numbers: 0, 1, 2, 3, ...
- Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Rational numbers: fractions and decimals
- Real numbers: all rational and irrational numbers
Operations:
- Addition and subtraction: combining numbers
- Multiplication and division: repeated addition and subtraction
- Order of operations: PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction)
Properties of Operations:
- Commutative property: order of numbers does not change result
- Associative property: order of operations does not change result
- Distributive property: multiplying a number by a sum is the same as multiplying by each addend

Variables and Expressions:
- Variable: a symbol representing a value that can change
- Expression: a group of numbers, variables, and operations
Equations and Inequalities:
- Equation: a statement that two expressions are equal
- Inequality: a statement that two expressions are not equal
- Solving equations and inequalities using various methods (e.g., addition, subtraction, multiplication, division)
Functions:
- Function: a relation between a set of inputs and a set of possible outputs
- Domain and range: input and output values of a function
- Types of functions: linear, quadratic, exponential, etc.

Basic Concepts:
- Experiment: an action that produces a set of outcomes
- Outcome: a result of an experiment
- Sample space: the set of all possible outcomes
Probability Measures:
- Theoretical probability: the number of favorable outcomes divided by the total number of outcomes
- Experimental probability: the number of times an event occurs divided by the total number of trials
- Probability rules: addition, multiplication, and complement
Independent and Dependent Events:
- Independent events: the occurrence of one event does not affect the other
- Dependent events: the occurrence of one event affects the other
- Conditional probability: the probability of an event occurring given that another event has occurred

A point has no size, only location
A line extends 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
Types of angles: acute, obtuse, right, straight, and reflex
Measurement units: degrees, radians, minutes, and seconds
Congruent figures have the same size and shape
Similar figures have the same shape, but not necessarily the same size
Symmetry types: line, rotational, and point symmetry
Perimeter is the distance around a shape
Area is the size of a shape's interior
Formulas exist for calculating perimeter and area of various shapes (e.g., triangles, quadrilaterals, circles)

Natural numbers: 1, 2, 3, ...
Whole numbers: 0, 1, 2, 3, ...
Integers: ..., -3, -2, -1, 0, 1, 2, 3, ...
Rational numbers: fractions and decimals
Real numbers: all rational and irrational numbers
Addition and subtraction combine numbers
Multiplication and division are repeated addition and subtraction
Order of operations: PEMDAS (parentheses, exponents, multiplication and division, addition and subtraction)
Commutative property: order of numbers does not change result
Associative property: order of operations does not change result
Distributive property: multiplying a number by a sum is the same as multiplying by each addend

A variable is a symbol representing a value that can change
An expression is a group of numbers, variables, and operations
An equation is a statement that two expressions are equal
An inequality is a statement that two expressions are not equal
Equations and inequalities can be solved using various methods (e.g., addition, subtraction, multiplication, division)
A function is a relation between a set of inputs and a set of possible outputs
Domain and range are input and output values of a function
Types of functions: linear, quadratic, exponential, etc.

An experiment is an action that produces a set of outcomes
An outcome is a result of an experiment
Sample space is the set of all possible outcomes
Theoretical probability is the number of favorable outcomes divided by the total number of outcomes
Experimental probability is the number of times an event occurs divided by the total number of trials
Probability rules: addition, multiplication, and complement
Independent events: the occurrence of one event does not affect the other
Dependent events: the occurrence of one event affects the other
Conditional probability is the probability of an event occurring given that another event has occurred