MATH+

• Axiom - a statement or proposition which is regarded as being established or self-evidently true
• Undefined Terms - terms that we cannot precisely define but were accepted by its definition
• Defined Terms - has a formal definition
• Axioms/Postulates - statements which are accepted as true without proof
• Theorems - statement that can be proven
• Line - set of infinite points extending in two directions
• Collinear Points - points that belong in the same line
• Non-Collinear Points - points that do not belong in the same line
• Coplanar Points - points that belong in the same plane
• Non-Coplanar Points - points that do not belong in the same plane
• Reflexive Property - a quantity is equal to itself
• Symmetric Property - if A=B, then B=A
• Transitive Property - If A=B and B=C, then A=C
• Addition Property of Equality - If A=B, then A+C = B+C
• Properties/Axioms

  • Reflexive Property
  • Symmetric Property
  • Transitive Property
  • Addition Property of Equality
• Postulate 1 - a line contains atleast 2 points
• Postulate 2 - a plane contains atleast 3 non-collinear points
• Postulate 3 - through any two points, there is exactly one line
• Postulate 4 - through any three non-collinear points, there is exactly one plane
• Theorem 1 - if two lines intersect, then they intersect at exactly one point
• Theorem 2 - if a point lies outside a line, then exactly one plane contains both line and the point
• Theorem 3 - if two lines intersect, then exactly one plane contains both lines
• Angle Addition Postulate - if a point lies on the interior of an angle, then that angle is the sum of two smaller angles with legs that go through the given point

  
• Postulate 5 - if two points lie on the same plane, then the line joining them lies in that plane

  
• Postulate 6 - if two planes intersect, then their intersection is a line

  
• Corresponding Angles Postulate - if a transversal intersects two parallel lines, the pairs of corresponding angles are congruent

  
• Parallel Postulate - given a line and a point not on that line, there exists a unique line through the point parallel to the given line

  
• Alternate Exterior Angles Theorem - if a transversal intersects two parallel lines, then the alternate exterior angles are congruent

  
• Alternate Interior Angles Theorem - if a transversal intersects two parallel lines, then the alternate interior angles are congruent

  
• Same Side Interior Angles Theorem - if a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are SUPPLEMENTARY

  
• Vertical Angles Theorem - if two angles are vertical angles, then they have equal measures

  
• Triangle - has an interior angle of 180 degrees
• CPCTC - Corresponding Parts of the Triangle are Congruent
• CPCTC - two triangles are said to be congruent if and only if their corresponding parts are congruent
• Triangle Sum Theorem - sum of three interior angles is always equal to 180 degrees
• Isosceles Triangles - two sides of equal length but the third side or base may be of different length
• Isosceles Triangle Theorem - if two sides of a triangle are congruent, then angles opposite those sides are congruent
• Right Angle Theorem - states that all right angles are congruent
• Hypotenuse - the side opposite the right angle or the longest side
• ASA Congruence Theorem

  • Angle-Side-Angle Theorem
  • if any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two are congruent