# Construct parallel lines using perpendicular bisectors

- Author:
- mark vasicek

## STUDENTS:

Construct two lines through point C
One must be parallel to the given line, AB.
The other must be perpendicular to the given line AB.
Submit (bottom of the page).
Need more help, see instructions below.
Still stuck? See video.

## Detailed Instructions

Start with a given line AB, and point C not on that line.
Construct a circle with center at C and radius CB. (Drag from center to the radius).
The circle should pass through the given line in 2 places.
Mark the second intersection, point D.
Point C is the same distance from B and D.
You want to find another point, like C, that is the same distance from B and D.
Construct two circles, with center at B and radius BD, center at D radius BD.
These two circles will intersect twice.
Use the intersect tool to select both these circles. You get their intersections are points E and F.
Construct line EF.
Notice how this line passes through point C and is perpendicular to AB (our given line), and it bisects (cuts into two equal parts) segment BD.
That is the first part of what we're trying to do!
Now, we need to make a line parallel to the given line that passes through C.
This will also be perpendicular to line EF.
You have circle C with radius CB.
Use the intersection tool to construct the two points where circle C intersects line EF.
These will be labeled G and H.
These two points are the same distance from C. They are radii of circle C: CG and CH.
Construct two circles, center at G and radius GH, center at H and radius HG.
Use the intersect tool to mark where those two circles intersect.
These will be points I and J.
Construct line IJ.
Do the drag test.
And now you have:
An original line AB and point C not on that line.
AND
A line that passes through C that is perpendicular to AB.
AND
A line that passes through C that is parallel to AB.