GFCP - Geometric Constructions Lesson

Geometric Constructions

Note: You will need a compass and straight edge for this lesson. You may use online versions.

Before sophisticated tools were used, builders had to use the materials available to lay out and measure buildings and monuments. A commonly used tool was a length of rope. You could tie knots in the rope to represent a given distance and by pulling a rope tight, you could make a straight line. In Geometry class, we can imitate the use of rope by using a compass to measure distance and a straight edge to help us draw straight lines. We can then use these simple tools to construct geometric figures which are perfectly drawn.

When we construct a square, it will definitely have four (4) congruent sides and four (4) right angles, but it will not just look like a square. We will know that it is indeed a square by the marks we made with our compass and straight edge.   Similar to the previous lesson, we will know our conclusion is true, based on the proof. 

image stating: "when performing a construction, we never measure with a ruler or protractor."

In this lesson you will learn how to perform the following constructions: Copying a segment; Constructing a rhombus; copying an angle; bisecting a segment; bisecting an angle; constructing a line parallel to a given line through a point not on the line; and constructing perpendicular lines, including the perpendicular bisector of a line segment. We will also construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

It sounds like a lot, but with a few simple techniques, you can do all of these and more!

In the following video, you will see how to copy a segment with a compass. You will then see that with this one simple construction you possess all you need in order to perform the other five (5) constructions.

  1. copying a segment
  2. copying and angle
  3. bisecting an angle
  4. constructing a line parallel to a given line through a point not on the line
  5. constructing a rhombus

Use your compass and straight edge (or this website: https://www.geogebra.org/geometry) to try these constructions yourself.

Now you will add one other technique, the construction of a perpendicular bisector. This will allow you to perform a few more constructions.

Lastly, you will learn how to inscribe three geometric figures inside a circle.

 

Constructing an Angle Bisector

First, we need to learn how to construct an angle bisector. Watch the video below and follow along on your own paper to practice.

Constructing a line parallel to a given line through a point NOT on the line.

We also need to know how to construct a parallel line to a given line through a point NOT on the line.  

Steps for Constructing a Parallel Line through a point NOT on the line

  1. Start with a line (with two points labeled A and B) any point, not on the line (point C).
  2. Construct Ray AC.
  3. Construct a circle centered at point A with radius AB. Mark the intersection of the circle and Ray AC; label it point D.
  4. Copy the circle with radius AB and center it at point C. Mark the intersections of the circle and Ray AC; label them point E and point F.
  5. Construct a circle centered at point B with radius BD. 
  6. Copy the circle with radius BD and center it at point F.
  7. Mark the intersections of circle F and circle C; label them point G and point H.
  8. Construct Ray CH.

IMAGES CREATED BY GAVS