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Perpendiculars and Distance Honors Geometry Chapter 3, Section 6 GeoGebra Draw a line a, Draw a point off the line, C Add a point on the line, D Draw a segment between C and D Measure the segment Measure the angle BDC, select the points in exactly that order. Drag point D to make the length of CD the shortest possible What do you notice about angle BDC Notes The shortest distance between a point and a line is always the length of the perpendicular segment from the point to the line. Whenever we refer to the distance between lines or points and lines, we are talking about this shortest perpendicular distance. Notes Parallel lines are everywhere equidistant i.e. the distance between parallel lines is the same everywhere. In a plane, if two lines are equidistant from a third line, then they are parallel to each other (Theorem)