1. 2.8 Proving Angle Relationships What you’ll learn: 1.To write proofs involving supplementary and complementary angles. 2.To write proofs involving congruent and right angles.

2. Postulates Postulate 2.10 – Protractor Postulate – angles can be measured using a protractor. Postulate 2.11 – Angle Addition Postulate If R is in the interior of  PQS, then m  PQR+m  RQS=m  PQS If m  PQR+m  RQS=m  PQS, then R is in the interior of  PQS. P Q R S

3. Theorems 2.3 Supplement Theorem – If 2  s form a linear pair, then they are supplementary  s. 2.4 Complement Theorem – if the noncommon sides of 2 adjacent  s form a right , then the  s are complementary  s. 2.5.Congruence of  s is reflexive, symmetric, and transitive. Reflexive:  A  A Symmetric: If  A  B, then  B  A Transitive: If  A  B and  B  C, then  A  C. 2.6 Angles supplementary to the same angle or to congruent angles are congruent.

4. More Theorems 2.7 Angles complementary to the same angle or to congruent angles are congruent. 2.8 If 2 angles are vertical angles, then they are congruent. 2.9 Perpendicular lines intersect to form 4 right angles. 2.10 All right angles are congruent. 2.11 Perpendicular lines form congruent adjacent angles 2-12 If 2  s are  and supplementary, then each  is a right . 2-13 if 2   s form a linear pair, then they are right  s.

5. Don’t forget Definition of supplementary angles – if 2 angles are supplementary, they add to be 180 . Definition of complementary angles – if 2 angles are complementary, they add to be 90 . Definition of congruent angles: if 2 angles are congruent, they are equal in measure and vice-versa. Definition of angle bisector – an angle bisector creates 2 congruent angles. Definition of right angles – if an angle is right, its measure is 90 

6. Find the measure of each numbered angle. 1.  1=65,  2=? 2.  1=32,  2=?,  3=? 3.  1=125,  2=?,  3=?,  4=? 4.  4=x-32,  2=175-2x 12 1 2 3 1 2 3 4 1 2 3 4

7. Sometimes, always, never 1.Supplementary angles are congruent. sometimes 2.If 2 angles form a linear pair, then they are complementary. never 3.Two vertical angles are supplementary. sometimes 4.Two angles that are congruent to the same angle are congruent to each other. always

8. Write a 2-column proof. Given:  ABC is a right angle. Prove:  1 and  2 are complementary angles 1.  ABC is a right angle. 2.m  ABC =90 3.m  ABC =m  1+m  2 4.90=m  1+m  2 5.  1 and  2 are complementary angles Given defn. right angles Angle addition postulate Substitution Defn of comp. angles 1 2 A B C

9. Homework p. 112 16-32 even, 38, 46-54 even