Exams

• Supplementary Angles


  If the sum of the measures of two angles is 180°, then they are called supplementary angles
• Complementary Angles


  If the sum of the measures of two angles is 90°, then they are called complementary angles
• It is not necessary for two angles to be adjacent to be called supplementary or complementary
• Linear Pair of Angles


  A pair of adjacent angles whose noncommon sides are collinear. The sum of the measures of the angles is 180°.
• Common Vertex


  The point where the angles meet.
• Common Side


  The line that the angles share.
• No Common Interior Points

  The angles do not overlap.
• Adjacent Angles

  Two angles with a common vertex, a common side, and no common interior points.
• Vertical Angles

  Pair of angles opposite each other formed by two intersecting lines in an "X"-shape. Vertical angles are equal in measure and so are congruent
• Triangle

  The union of three segments determined by three non-collinear points
• Parts of a triangle

  • Vertices
  • Sides
  • Angles
• Right triangle


  • A triangle with a right angle, composed of two legs and a hypotenuse
• Acute triangle

  • A triangle with three acute angles
• Obtuse triangle

  • A triangle with an obtuse angle
• Equiangular triangle

  • A triangle with three equal angles
• Equilateral triangle

  • A triangle with three equal sides
• Isosceles triangle

  • A triangle with two equal sides
• Scalene triangle

  • A triangle with no equal sides
• Elimination method

  Solving systems of equations by adding the equations when the coefficients of the same variable are additive inverses
• Elimination method steps

  1. Add the equations

  2. Substitute the x value into one of the original equations to find y
• You can substitute the x and y values in the equations to verify if the solution is correct
• Substitution method


  Solving systems of equations by substituting for a variable
• Substitution method steps

  1. Substitute one variable in terms of the other

  2. Solve for one variable

  3. Substitute the value back into one of the original equations to find the other variable
• Point


  A point has no dimension, it is represented by a small dot
• Line

  A line has no width and extends endlessly in both directions, it has one dimension: length
• Plane

  A plane is a flat surface that extends infinitely far in all directions, it has no thickness
• Space

  A space is the set of all points, it extends infinitely in all directions and has three dimensions
• Collinear points

  Points on the same line
• Coplanar points

  Three or more points on the same plane
• Coplanar lines

  Lines on the same plane
• Geometric Terms

  • Point
  • Line
  • Plane
  • Space
  • Collinear Points
  • Coplanar Points
  • Coplanar Lines
• The point, line, and plane are the seed concepts of geometry. They are often called "undefined terms".
• Postulates are statements of facts or self-evident truths, accepted as true without proof.
• Basic Postulates

  • Points Postulate: A line contains at least two points
  • Line Postulate: A plane consists of at least three non-collinear points
  • Plane Postulate: A space contains at least four non-coplanar points
  • Flat Plane Postulate: Two points determine a line, three non-collinear points determine a plane
  • Plane Intersection Postulate: If two planes intersect, then their intersection is a line
  • Ruler Postulate: There is one and only one positive real number called the distance between two points
  • Segment Construction Postulate: On any ray, there is exactly one point at a given distance from the endpoint of the ray
  • Segment Addition Postulate: If point P is between A and B, then the linear measures AP+PB=AB
• Theorems are statements that must be proven true by citing undefined terms, definitions, postulates, and other proven theorems.
• Basic Theorems

  • Line Intersection Theorem: If two lines intersect, then their intersection is exactly one point
  • Line-Point Theorem: Given a line and a point not on the line, there is exactly one plane that contains them
  • Line-Plane Theorem: Given two intersecting lines, there is exactly one plane that contains the two lines
  • Line-Plane Intersection Theorem: Given a plane and a line not on the plane, their intersection is one and only one point
• Segment

  A line segment formed by connecting two distinct points A and B, denoted as AB or BA
• Congruent segments

  • Segments with equal measures
• A segment has exactly one midpoint
• Bisector of a segment

  A set of points whose intersection with the segment is the midpoint of the segment