2 8 Proving Angle Relationships What youll learn

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.

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 P interior of PQS. R Q S

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.

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.

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

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

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

Write a 2 -column proof. A 1 C B Given: ABC is a right angle. Prove: 1 and 2 are complementary angles 1. 2. 3. 4. 5. ABC is a right angle. m ABC =90 m ABC =m 1+m 2 90=m 1+m 2 1 and 2 are complementary angles 2 Given defn. right angles Angle addition postulate Substitution Defn of comp. angles

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