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Perpendiculars and Distance

Explore the concepts of perpendicularity and distance in geometry with this interactive lesson using GeoGebra. This section focuses on drawing a line and points, measuring line segments, and understanding angles formed by these elements. You'll learn that the shortest distance between a point and a line is the length of the perpendicular segment. Additionally, we discuss properties of parallel lines and equidistant lines that indicate parallelism. Engage with practical activities to visualize and solidify your understanding of these geometric principles.

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Perpendiculars and Distance

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  1. Perpendiculars and Distance Honors Geometry Chapter 3, Section 6

  2. 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

  3. 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.

  4. 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)

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