Geometric Constructions In this lesson, you learned how a compass and straightedge are used to create constructions related

Geometric Constructions

In this lesson, you learned how a compass and straightedge are used to create constructions related to circles. In this assignment, you will use those tools to complete those constructions on your own.

As you complete the assignment, keep this question in mind:

How do you perform constructions related to circles?

Directions

Complete each of the following constructions, reading the directions carefully as you go. Be sure to show all work and insert an image of each construction. If you are unable to take and insert screenshots of the constructions, print this activity sheet and create them by hand using a compass and straightedge.

Your teacher will give you further directions about how to submit your work. You may be asked to upload the document, e-mail it to your teacher, or print it and hand in a hard copy.

Now, let’s get started!   

Step 1: Construct a circle through three points not on a line.

a) Construct a circle through three points not on a line using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a circle through three points not on a line by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

Step 2: Construct regular polygons inscribed in a circle.

a) Construct an equilateral triangle inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct an equilateral triangle inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

b) Construct a regular hexagon inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a regular hexagon inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)
  

c) Construct a square inscribed in a circle using the construction tool. Insert a screenshot of the construction here. Alternatively, construct a square inscribed in a circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

Step 3: Construct tangent lines to a circle.

a) Constructa tangent to a circle through a point on the circle using the construction tool. Insert a screenshot of the construction here. Alternatively, a tangent to a circle through a point on the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)

b) Construct a tangent to a circle through a point outside the circleusing the construction tool. Insert a screenshot of the construction here. Alternatively, construct a tangent to a circle through a point outside the circle by hand using a compass and straightedge. Leave all circle and arc markings. (10 points)