Chapter 1: Essentials of Geometry Section 1.5: Describe Angle Pair Relationships

Section 1.5: Describe Angle Pair Relationships Goals: Find the measures of angles formed by intersecting lines.

Section 1.5: Describe Angle Pair Relationships Complementary Angles: two angles in which the measures have the sum of 90º 70º 20º A B C D < ABC and < CBD are complementary angles

Supplementary Angles: two angles in which the measures have the sum of 180º Linear Pair: Two adjacent angles in which their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles T 80º 100º U S R < RST and < TSU are supplementary angles

Congruent Angles: angles that have the same measure Adjacent Angles: two angles that have a common vertex and a common side Congruent Angles: angles that have the same measure Common side C < CAT and < TAB are adjacent angles T A B Common Vertex 85º 85º Symbol for congruent:

Theorem: Congruent Complements Theorem: If two angles are complementary to the same angle, then they are congruent. 2 3 1 If < 1 & < 2 are complements, and < 2 and < 3 are complements, then < 1 ≅ < 3

Theorem: Congruent Supplements Theorem: If two angles are supplementary to the same angle, then they are congruent. 5 6 4 If < 4 & < 5 are supplements, and < 5 and < 6 are supplements, then < 4 ≅ < 6

Section 1.5: Describe Angle Pair Relationships Vertical Angles: When two lines intersect, the two angles that are not adjacent are vertical (across from each other) _____ and ______ are vertical angles. 2 1 3 4

Section 1.5: Describe Angle Pair Relationships Linear Pair: Two adjacent angles are a linear pair if their noncommon sides are on the same line. _____ and ______ are a linear pair. Linear Pair Postulate: If two angles form a linear pair, then they are supplementary. 5 6

Section 1.5: Describe Angle Pair Relationships Vertical Angles Theorem: Vertical angles are congruent What does this tell us? 2 1 3 4

Section 1.5: Describe Angle Pair Relationships Find the angle measures: (2x +11)° (5x – 7)° (7y +24)°

Section 1.5: Describe Angle Pair Relationships Try Together: Pg. 35 #1-7 (all) Homework: Pg. 38 #2-44 (even)