Perpendicular Through a Point NOT on a Line

Explore the construction of a perpendicular line through a point NOT on a line.

Summarize the properties and construction of perpendicular lines, points, and circles. Hint: If you are not familiar with the construction steps necessary for the perpendicular line through a point NOT on the line construction, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.


Construct a perpendicular line to line AB through point C by following the construction steps provided below.

Construction Steps:

1.Toolbar ImageConstruct another point on line AB. (point D) 5.Toolbar ImageCreate circle DE. (Circle e)
Hint:Be sure to test that when you move point D it stays attached to line AB. 6.Toolbar ImageConstruct the intersection points between circles d & e. (points F & G)
2.Toolbar ImageCreate circle CD. (Circle c) 7.Toolbar ImageCreate line FG. (line g)
3.Toolbar ImageConstruct the second intersection point between circle c and line AB. (point E) Toolbar ImageYou can construct segment EF and FD to explore their relationship.
4.Toolbar ImageCreate circle ED. (Circle d) Toolbar ImageYou can also construct segment EG and GD to explore their relationship.