1. Section 2.5: Proving Angles Congruent Objectives: Identify angle pairs Prove and apply theorems about angles

2. Important Angle Pairs  Vertical Angles: two angles whose sides are opposite rays (formed by the intersection of two lines)

3.  Adjacent Angles: Two coplanar angles with a common side, a common vertex, and no common interior points.

4.  Complementary Angles: Two angles whose measures have a sum of 90°. Each angle is called the complement of the other. Examples:

5.  Supplementary Angles: Two angles whose measures have a sum of 180°. Each angle is called the supplement of the other. Examples:

6. Linear Pair:  2 adjacent angles that form a line  They are supplementary (=180°) (x+20)°x°

7. Identifying Angle Pairs 1  Identify pairs of numbered angles that are: a.) complementary: b.) supplementary: c.) vertical: d.) adjacent: 5 3 4 2

8. Drawing Conclusions There are conclusions you can make from a diagram. You can assume that angles are…  Adjacent angles  Adjacent supplementary angles  Vertical angles Unless it is marked or you are told, you cannot assume…  Angles or segments are congruent  An angle is a right angle  Lines are parallel or perpendicular

9. Theorem:  A statement that is proved to be true  An acceptable justification to use in proofs We have several theorems in Geometry….

10. Theorem 2 -1: Vertical Angle Theorem  Vertical angles are congruent.

11. Theorem 2-2: Congruent Supplements Theorem  If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent.

12. Theorem 2-3: Congruent Complements Theorem  If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.

13. Theorem 2-4  All right angles are congruent

14. Theorem 2-5  If two angles are congruent and supplementary, then each is a right angle.

15. Find the value of the variable. 1. 2. 126° (3x)°(6x-54)° (8t)° (10t)°

16. Type 2: Use complete sentences  Point out 2 things that are incorrect in the diagram below 60° 120° 130° 50°