Construction 7

Author:: Bill Doherty

Construction 7 - Given a point not on a given line, construct the line parallel to the given line through the given point.

GeoGebra Applet

1. Use the line tool to construct line AC. 2. Construct Circle A as follows:

Select the "Circle with Center through Point" tool.
Tap on Point A.
Tap on a point on Line AC somewhere between Points A and C.
If not already labeled, label the point where this circle intersects the line (between A and C) as Point D.

3. Construct Circle C as follows:

Select the Compass tool.
Tap (in order) on Points A and D (to establish the length of the radius), then on Point C (to establish the center).

4. Construct the intersections of line AC and Circle C as follows:

Select the Intersect tool.
Select Line AC and Circle C.
This should have created two points of intersection. If they are not already labeled, label the intersection point between Points A and C as Point E and label the other intersection point as Point F.

5. Construct the intersections of line AB and Circle A as follows:

Select the Intersect tool.
Select Line AB and Circle A.
This should have created two points of intersection. If they are not already labeled, label the intersection point between Points A and B as Point H and label the other intersection point as Point G.

6. Construct Circle F as follows:

Select the Compass tool.
Tap (in order) on Points D and H (to establish the length of the radius), then on Point F (to establish the center).

7. Construct the intersections of Circles C and F as follows:

Select the Intersect tool.
Select Circles C and F.
This should have created two points of intersection. If they are not already labeled, label the intersection point on the same side of Line AC as Point G as Point I and label the other intersection (on the same side of Line AC as Point H) as Point J.

8. Use the Line tool to construct Line CJ by tapping on Points C and J. 9. Drag around Points A, B and C and observe what happens.