1. Angle Pair Relationships Geometry BCHS

2. I can: Identify vertical angles and linear pairs. Use vertical angles and linear pairs to find measures of angles.

3. Which angles are adjacent? 1 3 2 4  1 &  2,  2 &  3,  3 &  4,  4 &  1 Vertical Angles – 2 angles that are not adjacent and their sides are formed by two intersecting lines.  1 &  3,  2 &  4 Then what do we call  1 &  3?

4. Linear Pair (of angles) 2 adjacent angles whose non- common sides are opposite rays They make a line!!!! 1 2

5. Example Vertical angles?  1 &  4 Adjacent angles?  1 &  2,  2 &  3,  3 &  4,  4 &  5,  5 &  1 Linear pair?  5 &  4,  1 &  5 Adjacent angles not a linear pair?  1 &  2,  2 &  3,  3 &  4 1 3 2 5 4

6. Important Facts Vertical Angles Theorem-Vertical Angles are congruent. Linear Pair Postulate-The sum of the measures of the angles in a linear pair is 180 o.

7. Example: If m  5=130 o, find m  3 = m  6 = m  4 = 5 3 4 6 130° 50°

8. Example: Find x & y, then find: m  ABE m  ABD m  DBC m  EBC 3x+5 o y+20 o x+15 o 4y-15 o x=40 y=35 m  ABE=125 o m  ABD=55 o m  DBC=125 o m  EBC=55 o A B C D E