Math - 3rd cycle

• Conditional statement


  A logical statement that has two parts: IF (hypothesis/antecedent/premise) and THEN (conclusion)
• Hypothesis


  • Antecedent or premise (P)
• Conclusion


  • Consequence (Q)
• Types of conditional statements

  • Prime (only one factor)
  • Composite (two or more factors)
• Even


  Not divisible by 2
• Odd


  Divisible by 2
• Inverse


  not p + not q
• Converse


  q + p
• Contrapositive


  not q + not p
• Conditional


  P + Q
• Euclid


  First described geometry as a mathematical system through his textbooks
• Geometry refers to a structure formed from a set of undefined, definitions (defined terms), accepted properties, theorems, and axioms
• Mathematical system


  A structure formed from a set of undefined terms or agreements, valid definitions, accepted properties, and postulates which you can apply to derive new concepts, properties, and theorems through deductive reasoning
• Important parts of a mathematical system

  • Undefined terms
  • Definitions
  • Postulates
  • Accepted properties
  • Accepted theorems
• Undefined terms


  Do not have formal definitions, can only describe their features
• Definition


  A statement that describes the meaning of known words
• Collinear points


  Points that lie on the same line
• Coplanar points


  Points that lie on the same plane
• Ray


  Has one endpoint and extends infinitely in one direction
• Intersection points


  The collection of common points between two or more geometric figures
• Betweenness of a point


  If three points are collinear, then one point is between the other two points
• Congruent segments


  Two line segments that have the same length
• Coplanar Points


  Points that lie on the same plane
• Line Segment


  The union of points A, B, and all the points between them
• Ray


  Has an endpoint and extends infinitely in one direction
• Intersection Points


  The collection of common points between two or more geometric figures
• Distance between Two Points


  The length of the line segment that connects the two points
• Midpoint


  The point that divides a line segment into two congruent line segments
• Segment Bisector


  A point, ray, line segment, line, or plane that intersects the line segment at its midpoint
• Angle


  The union of two noncollinear rays with a common endpoint, where the rays are the sides of the angle and the common endpoint is the vertex
• Acute Angle


  An angle that measures greater than 0 but less than 90 degrees
• Right Angle


  An angle that measures exactly 90 degrees
• Obtuse Angle


  An angle that measures greater than 90 but less than 180 degrees
• Straight Angle


  An angle that measures exactly 180 degrees
• Congruent Angles


  Two angles with equal measures
• Angle Bisector


  A ray that divides an angle into two congruent angles
• Complementary Angles


  Two angles whose measures sum to 90 degrees
• Supplementary Angles


  Two angles whose measures sum to 180 degrees
• Adjacent Angles


  Two angles that share a common vertex and side, but have no common interior points
• Linear Pair


  Two adjacent angles whose noncommon sides are opposite rays