2.6 Prove Statements About Segments and Angles

Vocab Proof: a logical argument used to show something is true Two column proof: a numbered statement and corresponding reason that shows an argument in a logical order Theorem: a statement that can be proven

Theorems

Two column proof

Given: <1 and < 2 are complementary Prove: m<2 = 16 Statement Reason m<2 = 74 <1 and <2 are complementary m<1 + m<2 = 90 m<1+ 74 = 90 M<1 = 16 Given Given Def complementary angles Substitution Subtraction

Given: <1 and <2 are supplementary m<2 = 145 Prove m<1 = 35 <1 and <2 are supplementary m<2 = 145 m<1 + m<2 = 180 m<1 + 145 = 180 m<1 = 35 Given Given Def of supplementary angles Substitution Subtraction

Given: m<N = 42 m<L = 116 Prove: m<M = 22 m<L + m<M + m<N = 180 m<N = 42 m<L = 116 42 + m<M + 116 = 180 m<M + 158 = 180 m<M = 22 The sum of the measures of the angles of a triangle is 180 Given Given Substitution Combine like terms Subtraction