*Supplementary Angles: Two angles that add up to *Complementary Angles: Two angles that add up to Linear Pair Theorem: If two angles forma linear pair, then they are supplementary. Angle Addition Postulate: If a point S lies in the interior of ∠ PQR, then ∠ PQS + ∠ SQR = ∠ PQR. Vocabulary

Segment Addition Postulate: If a point B lies on a segment AC, then AB + BC = AC. Definition of Midpoint: A point on a line segment that divides it into two equal parts (the halfway point of a line segment). Definition of an Angle Bisector: A line that divides an angle into two congruent angles. Vocabulary A B C

Write a justification for each step, given that A and B are supplementary and mA = 45°. Writing Justifications 1. A and B are supplementary. mA = 45° Given information 2. mA + mB = 180° Def. of supp s 3. 45° + mB = 180° Subst. Prop of = 4. mB = 135° Subtr. Prop of =

Example 1 Write a justification for each step, given that B is the midpoint of AC and AB  EF. 1. B is the midpoint of AC.Given information 3. AB  BC 2. AB  EF 4. BC  EF Def. of mdpt. Given information Trans. Prop. of 

Write a two-column proof. Writing a Two-Column Proof Given: 1 and 2 are supplementary, and 1  3 Prove: 3 and 2 are supplementary.

StatementsReasons 1 and 2 are supplementary. 1  3 Given m1 + m2 = 180°Def. of supp. s m1 = m3 m3 + m2 = 180° 3 and 2 are supplementary Def. of  s Subst. Def. of supp. s

Write a two-column proof. Given: 1 and 2 are complementary, and 2 and 3 are complementary. Prove: 1  3

StatementsReasons 1 and 2 are complementary. 2 and 3 are complementary. Given m1 + m2 = 90° m2 + m3 = 90° Def. of comp. s m1 + m2 = m2 + m3 m2 = m2 m1 = m3 Subst. Reflex. Prop. of = Subtr. Prop. of = 1  3 Def. of  s