1. Constructing Parallel and Perpendicular Lines
Geometry 3-7

2. Draw a line and a point on a piece of patty paper
Investigation

3. Investigation Fold a perpendicular through the point
Mark the line, what are the four angles?
Investigation

4. Fold another line perpendicular to the folded line, and through the point
Investigation

5. Investigation How could we check that the lines are parallel
Use the first folded line as a transversal, and check corresponding angles
Investigation

6. Constructing Parallel Lines
Investigation

7. Draw a line and a point not on the line on a sheet of printer paper
Try to construct a parallel line through this point with a compass and a straightedge
Investigation

8. How To Construct Parallel Lines
Begin with point P and line k.
How To Construct Parallel Lines
Draw an arbitrary line through point P, intersecting line k. Call the intersection point Q. Now the task is to construct an angle with vertex P, congruent to the angle of intersection. P k Q
Investigation

9. Center the compass at point Q and draw an arc intersecting both lines
Center the compass at point Q and draw an arc intersecting both lines. Without changing the radius of the compass, center it at point P and draw another arc P k Q
Investigation

10. Set the compass radius to the distance between the two intersection points of the first arc. Now center the compass at the point where the second arc intersects line PQ. Mark the arc intersection point R. P k Q R
Investigation

11. Line PR is parallel to line kQ
Investigation

12. Review Lesson 1-5

13. How to construct a perpendicular to a line through a specific point?

14. How to construct a perpendicular to a line through a specific point?
Now, create a bisector from these points
Perpendicular

15. Perpendicular

16. Perpendicular

17. Perpendicular

18. Perpendicular

19. Worksheet 3-8
All
Homework