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.

Task:

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

Construction Steps:

1.

Construct another point on line AB.
(point D)

5.

Create circle DE. (Circle e)

Hint:

Be sure to test that when you move point D it stays attached to line AB.

6.

Construct the intersection points between circles d & e.
(points F & G)

2.

Create circle CD. (Circle c)

7.

Create line FG. (line g)

3.

Construct the second intersection point between circle c and line AB.
(point E)

You can construct segment EF and FD to explore their relationship.

4.

Create circle ED. (Circle d)

You can also construct segment EG and GD to explore their relationship.