1. PROVING ANGLES CONGRUENT

2. Vertical angles Two angles whose sides form two pairs of opposite rays 1 2 3 4 The opposite angles in vertical angles are congruent. In this case angles 1 & 2 would be congruent and angles 3 & 4 would be congruent.

3. 1 2 3 4 Because angles 1 & 4 form a straight line as well as angles 3 & 2 we only have to know the measure of one angle to know all of the angle If angle 3 is 60 0, then angle 2 would be 120 0 because they make a straight angle of 180 0. Then angle 4 would be 60 0 being vertical to angle 3 and angle 1 would be 120 0 being vertical to angle 2 60 0 120 0 60 0 20 0

4. Adjacent angles Two coplanar angles with a common side, a common vertex, and no common interior points In other words, two angles share one of the same rays

5. Complementary angles Two angles whose measures have the sum of 90 0 Each angle is called the complement of the other 40 0 50 0 As you can see from the figures the two angles can be adjacent or they can be separated but the angles must add up to 90 0

6. Supplementary angles Two angles whose measures have the sum of 180 0 Each angle is called the supplement of the other Here again, they can be adjacent or they may be two separate angles but their measure will be 180 0 75 0 105 0

7. Identifying Angle Pairs 1 5 2 3 4 Name a set of complementary angles < 2 and < 3 A set of supplementary angles < 4 and < 5 < 3 and < 4 Vertical angles < 3 and < 5

8. AE F B C D Name the adjacent angles: If m<EFD = 27, what is the m<AFD 180 – 27 = 153

9. AE B C D Conclusions you can draw from the diagram Adjacent angles Adjacent supplementary angles Vertical angles F

10. AE B C D F Things you cannot assume Angles or segments that are congruent If an angle is a right angle Lines are parallel or perpendicular We can assume these if there are markings

11. 43 2 15 What can you conclude from this diagram? <1 and <2 Congruent <2 and <3 Adjacent <4 and <5 adjacent supplementary angles <1 and <4 vertical angles T P Q V W What conclusions can you make here?

12. Assignment Page 100 1 – 18 20 – 22 29 – 30 32 - 34