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

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

3. 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

4. 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

5. 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:

6. 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

7. 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

8. 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

9. 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

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

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

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