Perpendicular Through a Point on a Line

Explore the construction of a perpendicular line through a point on a line.

Summarize the properties and construction of perpendicular lines, points, and circles. Hint: If you are not familiar with the steps necessary for constructing a perpendicular line through a point on that line, 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 on line AB. (point D) 5.Construct a circle with the center at point E and radius of g+.5. (circle d)
Hint:Be sure to test that when you move point D it stays attached to line AB. 6.Construct a circle with the center at point D and radius of g+.5. (circle e)
2.Toolbar ImageConstruct a circle centered at C and through point D. (Circle c) 7.Toolbar ImageConstruct the intersection points between circles d & e. (points F & G)
3.Toolbar ImageConstruct the intersection point between circle c and line AB. (point E) 8. Toolbar ImageConstruct line GF. (line h)
4.Toolbar ImageConstruct a segment from point C to D. (segment g) Toolbar ImageYou can construct segment EF and FD to explore their relationship.