5 ExampleIfJustify each step.Angle Add. Post.SubSubSubt. Prop.Sub
6 Theorems Supplement Theorem Complement Theorem If two angles form a linear pair, then they are supplementary angles.Complement TheoremIf the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
7 Example Angles 6 & 7 form a linear pair. 3x + 32 + 5x + 12 = 180 Justify each step.Supplement Thm.3x x + 12 = 180Sub8x + 44 = 180Sub8x =Subt. Prop.8x = 136SubDivision Prop.x = 17Sub
8 Properties of Angle Congruence ReflexiveSymmetricTransitive
9 Theorem Congruent Supplement Theorem Abbreviation: Angles supplementary to the same angle or to congruent angles are congruent.Abbreviation:
10 Theorem Congruent Complements Theorem Abbreviation Angles complementary to the same angle or congruent angles are congruent.Abbreviation
11 Prove that the vertical angles 2 and 4 are congruent. Given:Prove:
12 Theorem 2.8 Vertical Angle Theorem If two angles are vertical angles, then they are congruent.
14 Right Angle Theorems Theorem 2.9 Theorem 2.10 Theorem 2.11 Perpendicular lines intersect to form 4 right anglesTheorem 2.10All right angles are congruent.Theorem 2.11Perpendicular lines from congruent adjacent angles.
15 Theorem 2.12If two angles are congruent and supplementary, then each angle is a right angle.Theorem 2.13If two congruent angles form a linear pair, then they are right angles.