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Geometry: Section 3.4 Proofs with Perpendicular Lines What you will learn: 1. Find the distance form a point to a line 2. Construct perpendicular segments 3. Prove theorems about perpendicular lines 4. Solve real life problems about perpendicular lines The distance from a point to a line is the length of the perpendicular segment from the point to the line. This perpendicular segment will be the shortest distance from the point to the line x1 x2 y1 y2 2 2 AC 3 1 3 1 AC 4 4 2 2 2 2 AC 16 16 32 Constructing Perpendicular Lines Example: Construct a line through point A that will be perpendicular to line m. The perpendicular bisector of a segment is a line which is perpendicular to the segment at its midpoint. Constructing a Perpendicular Bisector Example: Construct the perpendicular bisector of the segment. The following theorems all deal with perpendicular lines. 1)h || k , j h 2)2 is a right angle 1)Given 2) Def. of Perpendicular 3)m2 90 3) Def. of Right Angle 4)m2 m6 4) Correponding Angles Theorem )m6 90 5) Substitution )6 is a right angle ) Def. of Right Angle )jk ) Def. of Perpendicular HW: pp 152 – 154 / 3 – 5, 10, 16, 17 – 20, 25