Parallel and Perpendicular Lines — Practice Geometry Questions

By Allen Ma, Amber Kuang

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

    image0.png

    through Point C.

    image1.png

  2. Construct a line parallel to

    image2.png

    that passes through Point C.

    image3.png

Answers and explanations

  1. Here is the solution:

    image4.png

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

    image5.png

    twice.

    image6.png

    Place the compass point at both locations where the arcs intersect

    image7.png

    At each location, make an arc below

    image8.png

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

    image9.png

  2. Here is the solution:

    image10.png

    Draw a line from Point C through

    image11.png

    at an angle. Label the intersection Point D.

    image12.png

    Using a width about half of

    image13.png

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

    image14.png

    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.

    image15.png