Perpendiculars and
Distance
Honors Geometry
Chapter 3, Section 6
GeoGebra
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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
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The shortest distance between a point and a
line is always the length of the perpendicular
segment from the point to the line.
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Whenever we refer to the distance between
lines or points and lines, we are talking about
this shortest perpendicular distance.
Notes
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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)