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Ms. Andrejko Real World Postulates and Theorems Postulates 3.4 3.5 Theorems 3.5 3.6 3.7 3.8 Examples Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer 1. ∠3 ≅ ∠7 2. ∠9 ≅ ∠11 3. ∠2 ≅ ∠16 4. m∠5 + m∠12 = 180 Practice Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. 1. m∠BCG + m∠FGC = 180 2. ∠CBF≅∠GFH 3. ∠EFB ≅∠FBC 4. ∠ACD ≅∠KBF Examples Find x so that ℓ // m . Practice Find x so that ℓ // m . Examples Given: <1 and <2 are complementary, BC CD Prove: BA // CD STATEMENTS REASONS BC CD Given <ABC= <1+<2 Angle Addition Post. <1 and <2 are complementary Given <1+<2 = 90 <ABC = 90 BA BC BA // CD Def. of Complementary Transitive Def. of Perpendicular Perp. Transversal Converse Practice Given: <2 and <3 are supplementary Prove: AB // CD STATEMENTS 1. <2&<3 are supplementary <2 and <3 are consecutive AB // CD REASONS Given 2. Consecutive Interior Angles Theorem 3. Consecutive Interior Angles Converse