Parallel and Perpendicular Lines — Practice Geometry Questions

You can apply your knowledge of geometric constructions to solve a variety of problems. The following practice questions test your ability to construct parallel and perpendicular lines.

If you're drawing two arcs for a construction, make sure you keep the width of the compass (or radii of the circles) consistent, and make your arcs large enough so that they intersect.

Practice questions

1. Use the following diagram to construct a line perpendicular to

   

   through Point C.

   

2. Construct a line parallel to

   

   that passes through Point C.

   

Answers and explanations

1. Here is the solution:

   

   Place the compass point on C, and using any width, draw an arc that intersects

   

   twice.

   

   Place the compass point at both locations where the arcs intersect

   

   At each location, make an arc below

   

   Label the intersection of those arcs D and connect D to C.

   

2. Here is the solution:

   

   Draw a line from Point C through

   

   at an angle. Label the intersection Point D.

   

   Using a width about half of

   

   place the compass point at D and draw one large arc. Using the same compass width, do the same at Point C.

   

   Measure the width of the first arc. Using that same width, place the compass point at C and draw an arc intersecting the original arc you drew.

   Connect C to the point where the arcs intersect.