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Chapter 2 Section 6 Complementary and Supplementary Theorems and Planning a Proof 5 parts to proving a theorem 1) Statement of the theorem 2) Diagram illustrating the given information (or hypothesis) 3) A list of the given (hypothesis) 4) A list of what is to be proven (conclusion) 5) A series of conditionals with their reasons in logical order that lead from the given to the prove (the proof!!) Supplementary R‘s Theorem • If two angles are supplements of congruent angles (or the same angle),then the two angles are congruent Complementary R‘s Theorem • If two angles are complements of congruent angles (or the same angle),then the two angles are congruent Proof of Supplementary Theorem • If two angles are supplements of congruent angles (or the same angle),then the two angles are congruent Given: <1 and <2 are supp <3 and <4 are supp 1 <2 @ <4 Prove: 2 3 4 <1 @ <3 Hypothesis conclusion reason 1) None <1 and <2 are supp given <3 and <4 are supp <2 @ <4 2) If <1 and <2 are supp then m<1 + m<2 = 180 and <3 and <4 are supp 3) If m<1 + m<2 = 180 m<3 + m<4 = 180 o and m<3 + m<4 = 180 Def supplementary angles o o then m<1 + m<2 = m<3 + m<4 Transitive / substitution prop then m<1 = m< 3 or <1 @ <3 Subtraction property o 4) If m<1 + m<2 = m<3 + m<4 m<2 = (or m<2 = m< 4) m< 4 This is a test question : True or false?? If R A is complementary to R B and R B is complementary to R C then R A is complementary to R C False!! Counter example: let m R B = 30 then A & C’s sum is 120 When is this true? o When the measure of R B is 45 o Practice work • P63 we 1-17 all 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) definitions An example used to prove an if-then statement is false Another name for a statement written in the if then form The proposition being investigated A conditional in which the hypothesis and conclusion have been interchanged Reasoning proven using given information, definitions, postulates, and theorems already proven An adjacent pair of angles whose exterior sides are perpendicular A statement that contains the words “if and only if” An adjacent pair of angles whose exterior sides are opposite rays Two angles such that the sides of one angle are opposite rays to the sides of the other angle The statement in an argument that follows as a result of the hypothesis