Perpendiculars and Distance

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)