1. Measuring Angles

2. Geometry vs Algebra Segments are Congruent –Symbol [  ] –AB  CD –  1   2 Lengths of segments are equal. –Symbol [ = ] –AB = CD –m  1 = m  2

3. Angles Formed by 2 rays with the same endpoint –Vertex of the Angle Symbol: [  ] Name it by: –Its Vertex  A –A number  1 –Or by 3 Points  BAC - Vertex has to be in the middle A 1 B C

4. How many  s can you find? Name them. 3  s –  ADB or  BDA –  BDC or  CDB –  ADC or  CDA Notice D (the vertex) is always in the middle. Can’t use  D But  1 or  2 could be added. A B C D 1 2

5. Classifying Angles by their Measures Acute  Right  Obtuse  x°x° x < 90° x°x° x = 90° x°x° x > 90° Straight  x°x° x = 180°

6. Postulate 1-7 Protractor Postulate Let OA & OB be opposite rays in a plane, & all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180. ABO D C

7. Postulate 1-8 Angle Addition Postulate If point B is in the interior of  MAD, then m  MAB + m  BAD = m  MAD M B D A

8. If  MAD is a straight , then m  MAB + m  BAD = m  MAD = 180° m  MAB + m  BAD = m  MAD = 180° M B D A

9. Finding  measures (m  ) Find m  TSW if – m  RSW = 130° –m  RST = 100° R S T W m  RST + m  TSW = m  RSW 100 + m  TSW = 130 m  TSW = 30°

10.  Addition m  XYZ = 150  1 = 3x - 15  2 = 2x - 10 x Y Z m  1 + m  2 = m  XYZ (3x - 15) + (2x – 10) = 150 5x – 25 = 150 5x = 175 x = 35

11. Adjacent Angles Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points.

12. Vertical Angles Vertical angles – two angles whose sides are opposite rays.

13. Complementary Angles Complementary angles – two angles whose measures have a sum of 90°. –Each angle is called the complement of the other.

14. Supplementary Angles Supplementary angles – two angles whose measures have a sum of 180°. –Each angle is called the supplement of the other.

15. Identifying Angle Pairs Is the statement true or false? a. are adjacent angles. b. are vertical angles. c. are complementary.

16. Perpendicular Lines Perpendicular lines – intersecting lines that form right angles

17. Linear Pairs A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. –The angles of a linear pair form a straight angle.

18. Finding Missing Angle Measures are a linear pair. What are the measures of ?

19. Finding Missing Angle Measures

20. Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles. –Its endpoint is at the angle vertex. –Within the ray, a segment with the same endpoint is also an angle bisector. The ray or segment bisects the angle.

21. Using an Angle Bisector to Find Angle Measures bisects. If, bisects. If, what is what is