Geometry Basics

Geometry

• 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

Algebra

• 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

Geometry

• 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

Algebra

• 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