MATH

• Undefined terms


  Terms that cannot be precisely defined, can only be described or illustrated
• Defined terms


  Terms that have a formal definition, used to define even more terms
• Axioms/Postulates


  Statements accepted as true without proof, can be used as reasons in proving mathematical statements
• Theorems


  Statements that can be proven, can also be used as reasons in proving other statements
• Geometry is the visual study of shapes, sizes, patterns, and positions, occurring in all cultures through at least one of the five strands of human activities: Buildings/structures, Machines/motion, Navigating/star-gazing, Arts/patterns, Measurement
• Parts of a mathematical system

  • Undefined terms
  • Defined terms
  • Axioms/Postulates
  • Theorems
• Point


  Describes a location, has no size, represented by a dot
• Line


  Has infinite length, no width, nor thickness, extends infinitely in two opposite directions
• Plane


  Flat surface extending infinitely in all directions, has infinite length and width but no thickness
• Defined terms


  • Collinear points
  • Non-collinear points
  • Coplanar points
  • Non-coplanar points
• Subsets of a line


  • Line segment
  • Ray
  • Opposite ray
• Axiomatic system


  Set of axioms used to derive theorems
• Angle


  The union of two noncollinear rays with a common endpoint
• Vertex


  The point where two rays meet
• Legs


  The sides of an angle
• Interior and exterior angles


  Interior angles are on the inside of a shape, exterior angles are on the outside
• Adjacent angles


  Two angles sharing a common side and vertex
• Triangles


  A closed, two-dimensional shape and a plane figure with three straight sides and three angles. Triangles are often used in roof trusses because they offer strength and rigidity to support the roof, and they are considered one of the most important shapes in architecture and engineering. And unlike rectangles, a triangle cannot be deformed without changing the length of one of its sides or breaking one of its joints. Thus, we say that triangles are considered the most stable shape.
• Congruent triangles


  Have both the same shape and the same size. Congruent triangle are also two triangles that are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.
• Congruence


  Denoted by the symbol "≅" and read as "is congruent to"
• Undefined terms


  • Point
  • Line
  • Plane
• Congruent triangles


  Can be flipped, rotated and mirrored and will still be congruent
• SIDE-SIDE-SIDE (SSS) CONGRUENCE POSTULATE


  If the three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
• Point


  • Describes a location, has no size, represented by a dot
• SIDE-ANGLE-SIDE (SAS) CONGRUENCE POSTULATE


  If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
• ANGLE-SIDE-ANGLE (ASA) CONGRUENCE POSTULATE


  If two angles and the included side (a side in between the two marked angles) of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
• Line


  • Has infinite length, no width, nor thickness, extends infinitely in two opposite directions, represented by a straight line with two arrowheads
• ANGLE-ANGLE-SIDE (AAS) CONGRUENCE POSTULATE


  If two angles and a non-included side (a side not in between of the two marked angles) of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
• CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
• Plane


  • A flat surface extending infinitely in all directions, has infinite length and width but no thickness, usually represented by a four-sided figure
• Parallel lines


  Lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines.
• Transversal lines


  A line that can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points, then it is known as a transversal line.
• ALTERNATE INTERIOR ANGLES POSTULATE


  If a transversal line cuts two parallel lines, then alternate interior angles are congruent.
• ALTERNATE EXTERIOR ANGLES POSTULATE


  If a transversal line cuts two parallel lines, then alternate exterior angles are congruent.
• CORRESPONDING ANGLES POSTULATE


  If a transversal line cuts two parallel lines, then corresponding angles are congruent.
• SAME-SIDE INTERIOR ANGLES POSTULATE


  If a transversal line cuts two parallel lines, then same-side interior angles are supplementary.
• SAME-SIDE EXTERIOR ANGLES POSTULATE


  If a transversal line cuts two parallel lines, then same-side exterior angles are supplementary.
• Line segment


  A part of a line consisting of two endpoints and all the points in between
• Ray


  A portion of a line that has only one endpoint and extends infinitely in the other direction
• Opposite rays


  Rays with a common endpoint but extending in opposite directions