1. 1.6 Angle Pair Relationships Geometry Ms. Reser Fall 2005

2. Standards/Objectives : Standard 3: Students will understand geometric concepts and applications. Objectives: Identify vertical angles and linear pairs. Identify complementary and supplementary angles.

3. Assignment: pp. 47-49 #4-36 all; 41-51 odd

4. Which angles are adjacent? 1 3 2 4  1 &  2,  2 &  3,  3 &  4,  4&  1 Vertical Angles – 2 angles that share a common vertex & whose sides form 2 pairs of opposite rays.  1 &  3,  2 &  4 Then what do we call  1 &  3?

5. Linear Pair (of angles) 2 adjacent angles whose non- common sides are opposite rays. 1 2

6. 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

7. Important Facts Vertical Angles are congruent. The sum of the measures of the angles in a linear pair is 180 o.

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

9. Example: Find x y 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

10. Complementary Angles 2 angles whose sum is 90 o 1 2 35 o A 55 o B  1 &  2 are complementary  A &  B are complementary

11. Supplementary Angles 2 angles whose sum is 180 o 1 2 130 o 50 o X Y  1 &  2 are supplementary.  X &  Y are supplementary.

12. Ex:  A &  B are supplementary. m  A is 5 times m  B. Find m  A & m  B. m  A + m  B = 180 o m  A = 5(m  B) Now substitute! 5(m  B) + m  B = 180 o 6(m  B)=180 o m  B=30 o m  A=150 o