A pair of angles can sometimes be classified by their combined measures

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A pair of angles can sometimes be classified by
their combined measures

• These pairs are known as complementary and
  supplementary angles

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Complementary Angles

• 2 angles are complementary angles if the sum of
  their measures is 90 degrees.

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Supplementary angles

• 2 angles are supplementary angles if the sum of
  their measures is 180 degrees.

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• The sum of an angle and its complement is 90
  degrees.
• The sum of an angle and its supplement is 180
  degrees

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Theorem 6-1Congruent Complements Theorem

• If 2 angles are complementary to the same angle
  or to congruent angles, then they are congruent.

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Theorem 6-2Congruent Supplements Theorem

• If 2 angles are supplementary to the same angle
  or to congruent angles, then they are congruent

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ADJACENT ANGLES

• 2 angles in the same plane that share a vertex
  and a side, but share no interior points are
  adjacent angles.

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Linear Pair

• Adjacent angles whose non-common sides are
  opposite rays are a linear pair.
• A linear pair composes a straight line.
• Linear pairs are supplementary

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Theorem 6-3Linear Pair Theorem

• If 2 angles form a linear pair, then they are
  supplementary

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Vertical Angles

• Nonadjacent angles formed by 2 intersecting lines
  are vertical angles.
• Vertical angles share the same vertex and have no
  common sides

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Theorem 6-4Vertical angle Theorem

• If 2 angles are vertical angles, then they are
  congruent

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PERPENDICULAR BISECTOR

• A perpendicular bisector is a line, segment or
  ray that intersects a segment at its midpoint,
  forming 90 degree angles.
• Another way to define a perpendicular bisector is
  as a locus of points that are equidistant from
  the endpoints of a segment.

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THEOREM 6-5

• If a point lies on the perpendicular bisector of
  a segment, then the point is equidistant from the
  endpoints of the segment.

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THEOREM 6-6

• If a point is equidistant from the endpoints of a
  segment, then the point lies on the perpendicular
  bisector of the segment

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ANGLE BISECTOR

• An angle bisector is a line, segment or ray that
  divides an angle into 2 congruent adjacent angles

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THEOREM 6-7

• If a point lies on the bisector of an angle, then
  the point is equidistant from the sides of the
  angle.

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THEOREM 6-8

• If a point is equidistant from the sides of an
  angle, then the point lies on the bisector of the
  angle.