Angles

• An angle is the union of two rays that share a common endpoint

• The bisector of an angle is the ray that separates the given angle into two congruent angles.

  • There is one and only one bisector for a given angle.

• Protractor Postulate - The measure of an angle is a unique positive number

Angle Classification

• Acute angle
• Right angle
• Obtuse angle
• Straight angle
• Reflex angle

Angle Relationships

• Complementary angles are two angles with a sum of $90^{\circ }$
• Supplementary angles are two angles with a sum of $180^{\circ }$
• Two angles are adjacent if they have a common vertex and a common side between them.
• Congruent angles are two angles with the same measure

Intersection of Two Lines

• Vertical angles are the pair of congruent and opposing (non-adjacent) angles formed at the intersection of two lines.
  • Vertical angles are equal to each other

Line Intersects Two Lines

• Corresponding angles are angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
  • Corresponding angles formed between two parallel lines are equal to each other.
• Alternate angles are two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.
  • Alternate angles formed between two parallel lines are equal to each other.
• The sum of two same-sided angles between parallel lines is $180^{\circ }$.
• If there is equality of corresponding angles or alternate angles, or sum of two same-sided angles between the lines is $180^{\circ }$ then ${\ell }_2\parallel {\ell }_1$ or ${\ell }_1={\ell }_2$