CP - 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.
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.
- copying a segment
- copying and angle
- bisecting an angle
- constructing a line parallel to a given line through a point not on the line
- constructing a rhombus
Use your compass and straight edge (or use the link from the sidebar) 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.
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