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Vocabulary *Supplementary Angles: Two angles that add up to 1800. *Complementary Angles: Two angles that add up to 900. 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. B A C 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. Writing Justifications Write a justification for each step, given that A and B are supplementary and mA = 45°. 1. A and B are supplementary. mA = 45° Given information 2. mA + mB = 180° Def. of supp s 3. 45° + mB = 180° Subst. Prop of = 4. mB = 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 2. AB EF Given information 3. AB BC Def. of mdpt. 4. BC EF Trans. Prop. of Writing a Two-Column Proof Write a two-column proof. Given: 1 and 2 are supplementary, and 1 3 Prove: 3 and 2 are supplementary. Statements Reasons 1. 1 and 2 are supplementary. 1. Given 1 3 2. m1 + m2 = 180° of supp. s 2. Def. . = m3 3. m1 . 3. Def. of s 4. m3 + m2 = 180° 4. Subst. 5. 3 and 2 are supplementary 5. Def. of supp. s Write a two-column proof. Given: 1 and 2 are complementary, and 2 and 3 are complementary. Prove: 1 3 Statements Reasons 1. 1 and 2 are complementary. 1. Given 2 and 3 are complementary. 2. m1 + m2 = 90° m2 + m3 = 90° of comp. s 2. Def. . + m2 = m2 + m3 3. Subst. 3. m1 . 4. m2 = m2 4. Reflex. Prop. of = 5. m1 = m3 5. Subtr. Prop. of = 6. 1 3 6. Def. of s