Explore the construction of a parallel lines using the rhombus construction method.

Summarize the properties and construction of parallel lines, Rhombi, and circles.
Hint: If you are not familiar with the construction steps necessary for the rhombus method of constructing parallel lines, 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.

Construct the intersection point between circle d and line AB.
(point F)

Hint:

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

6.

Construct a circle centered at F and through point E. (Circle e)

2.

Construct a circle centered at C and through point D. (Circle c)

7.

Construct the intersection point between circle d and circle e.
(point G)

3.

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

8.

Construct line CG. (line g)

4.

Construct a circle centered at E and through point C. (Circle d)

You can also construct segment EC and FG to explore their relationship.