Perimeter, Area, and Volume: Lesson 2 - Properties of Circles

Properties of Circles is the second of seven self-paced lessons in the “Perimeter, Area, and Volume” section of KET’s GED® Geometry Professional Development Online Course. This lesson focuses on the properties of circles and guides students in recognizing a circle when it is embedded in a realistic setting or when parts of a circle are included in an irregular figure.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, students will apply their understanding of circles to solve problems.

They need to understand that a circle is a flat, closed figure in which every point is the same distance from the center.

They also need to be able to use the concepts of radius and diameter and the relationship between the two.

This lesson focuses on the properties of circles. A challenge of the GED Mathematics Test is that students need to recognize a circle when it is embedded in a realistic setting or when parts of a circle are included in an irregular figure (as in Lesson 5 of this module).

2Key Circle Concepts

A circle is a flat, closed figure with no angles or sides. A complete rotation around the center of a circle is 360 degrees (°).

Every point on a circle is the same distance from its center.

Question Which of these figures is a circle?

Step 1 Review the definition of a circle. Find the figures that are flat and closed.

Figures (2) and (5) are flat and closed, so they could be circles. Figures (1) and (3) have three dimensions, so they are not flat, and figure (4) is open.

Step 2 Check if the center is the same distance from every point on the figure. The center of the figure in choice (5) is not the same distance from every point, but the distance from center of choice (2) is.

Figure (5) is not a circle, figure (2) is a circle.

Answer figure (2)

3Radius and Diameter

The radius is the distance from the center of a circle to any point on the circle.

The diameter is the distance across a circle through the center. The diameter is always twice the length of the radius.

Question What is the diameter of the wheel in the image on the left?

Step 1 Find the length of the radius since the diameter is always twice the length of the radius.

radius = 13 inches

Step 2 Multiply the radius by 2 to find the diameter.

2 × 13 = 26

Answer 26 inches

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, also respond to the question below, which is related to building students’ skills.

How could you help students visualize the garden in Question 1?

Perimeter, Area, and Volume: Properties of Circles Skill Review

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Printable Resource

In this lesson you have learned about the properties of circles. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.

Assign directly to your students using the code or link above, without having them log in. Simply tell your students to go to
www.pbsstudents.org and enter the Assignment Code, or click on the Assignment URL to share the assignment as a link.