1. 1.5 Angle Relationships
Then: You measured and classified angles. Now: 1. Identify and use special pairs of angles 2. Identify perpendicular lines.

2. 19. Adjacent angles
Two angles that lie in the same plane, have a common vertex and side but no common interior points. Examples of adjacent angles:  DOC and  COB  AOB and  BOC Angles that are not adjacent:  DOC and  AOB

3. 20. Linear pair
A pair of adjacent angles whose noncommon sides are opposite rays. Example of a linear pair:  DAC and  CAB Angles that are not a linear pair:  DAC and  DAB

4. 21. Vertical Angles
Two nonadjacent angles formed by two intersecting lines. Examples of vertical angles  1 and  3  2 and  4 Vertical angles are congruent.

5. Example 1: Name an angle pair that satisfies each condition:
a. Two acute adjacent angles
 ______ and  ______
b. A linear pair
c. Two obtuse vertical angles

6. 22. Complementary Angles
Two angles with measures that have a sum of 90. Example complementary angles:  CBD and  DBE Complementary angles do not have to be adjacent.

7. 23. Supplementary Angles
Two angles with measures that have a sum of 180. Examples of supplementary angles:  ABC and  CBE  EFG and  GFH Supplementary angles do not have to be adjacent. Linear pair of angles are supplementary.

8. Example 1 continued: Name an angle pair that satisfies each condition:
d. Angle complementary to EKH
 ______
e. Angle supplementary to FKG

9. Example 2:
a. Find the measure of an angle and its complement if one angle measures 24 degrees more than the other. Sketch: Solution:

10. Example 2c: Find value of x and y.
1. Relationship between NSP and PSQ: 2. Relationship between NSQ and MSN: 3. Find value of x: 4. Relationship between NSQ and MSR: 5. Find value of y:

11. Example 2:
Find the value of the variable. e. mABC = (6x + 19) mCBD = (x) f. mABC = (5p + 28) mDBE = (12p)

12. 24. Perpendicular lines
Lines, segments, or rays that form four right angles.
Form congruent adjacent angles
Symbol: 
𝑨𝑬  𝑫𝑩

13. Example 3: Find x and y so that 𝑲𝑶 and 𝑯𝑴 are perpendicular.
2. Find y.

14. Interpreting Diagrams

15. Example 4:
Determine whether each statement can be assumed from the figure.
a. mVYT = 90.
b. TYW and TYU are supplementary.
c. VYW and TYS are adjacent.

16. 1.5 Assignment
p #8-40 evens, 43-45, 49, 50, 57-60