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Name:_____________________ Notes 3.6 Prove Theorems About Perpendicular Lines Distance from a point to a line _____________________________________________________________________ _____________________________________________________________________ Distance between two parallel lines _____________________________________________________________________ _____________________________________________________________________ THEOREM 3.8 If two lines intersect to form a linear pair of congruent angles, then the lines are ___________________. If l 2, then g ___ h. THEOREM 3.9 If two lines are perpendicular, then they intersect to form four __________. If a b, then l, 2, 3, and 4 are ______________. Example 1: Draw conclusions In the diagram at the right, 1 2. What can you conclude about a and b? THEOREM 3.10 If two sides of two adjacent acute angles are perpendicular, then the angles are ________________. If BA BC , then l and 2 are _______________. Example 2: Write a proof In the diagram at the right, l 2. Prove that 3 and 4 are complementary. Given l 2 Prove 3 and 4 are complementary. Statements Reasons___________ THEOREM 3.11 PERPENDICULAR TRANSVERSAL THEOREM If a transversal is perpendicular to one of two parallel lines, then it is ____________ to the other. If h || k and j h, then j ___ k. THEOREM 3.12 LINES PERPENDICULAR TO A TRANSVERSAL THEOREM In a plane, if two lines are perpendicular to the same line, then they are __________ to each other. If m p and n p, then m___ n. Example 3: Draw conclusions Determine which lines, if any, must be parallel in the diagram. Explain your reasoning. Example 4: Find the distance between two parallel lines What is the approximate distance from line m to line n? Example 5: Find the distance between point A (4, 1) and line t with equation y = x + 1. Example 6: Find the distance between the two parallel lines. Round to the nearest tenth, if necessary. Example 7: Find all unknown angle measures.