Lines and Angles

• Basic Geometric Terms

  • Point: Exact location, represented by a dot
  • Line: Extends infinitely in both directions ($\leftrightarrow$)
  • Line Segment: Part of a line with two end points ($--$)
  • Ray: Part of a line with one end point and one extending infinitely ($\rightarrow$)
  • Angle: Formed by two rays sharing a common endpoint (Vertex)

• Related Angles

  • Complementary Angles
    • Sum of measures is $90^\circ$
  • Supplementary Angles
    • Sum of measures is $180^\circ$
  • Adjacent Angles
    • Common vertex
    • Common arm
    • Non-common arms on opposite sides of common arm
  • Linear Pair
    • Adjacent angles whose sum is $180^\circ$
    • Form a straight line
  • Vertically Opposite Angles
    • Formed by two intersecting lines
    • Always equal in measure ($\angle 1 = \angle 3$)

• Pairs of Lines

  • Intersecting Lines
    • Meet at a single common point
    • Point of intersection
  • Transversal
    • A line that intersects two or more lines at distinct points
  • Parallel Lines
    • Lines that never intersect
    • Perpendicular distance between them is always the same

• Angles Made by a Transversal

  • Interior Angles
    • Angles lying inside the two lines ($\angle 3, \angle 4, \angle 5, \angle 6$)
  • Exterior Angles
    • Angles lying outside the two lines ($\angle 1, \angle 2, \angle 7, \angle 8$)
  • Corresponding Angles
    • Angles on the same side of the transversal and same relative position ($\angle 1 = \angle 5$)
  • Alternate Interior Angles
    • On opposite sides of the transversal, inside the lines ($\angle 4 = \angle 6$)
  • Alternate Exterior Angles
    • On opposite sides of the transversal, outside the lines ($\angle 1 = \angle 7$)
  • Interior Angles on the Same Side of Transversal
    • Also called Consecutive Interior or Co-interior angles
    • Sum is $180^\circ$ if lines are parallel

• Checking for Parallel Lines

  • Lines are parallel if:
    • Corresponding angles are equal
    • Alternate interior angles are equal
    • Interior angles on the same side of the transversal are supplementary