Unit 3, Lesson 2
Exploring Circles
Grade 7
2.1
Warm-up
Here are two figures.
Figure C looks more like Figure A than like Figure B. Sketch what Figure C might look like. Explain your reasoning.
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Here are two figures.
Figure C looks more like Figure A than like Figure B. Sketch what Figure C might look like. Explain your reasoning.
Your teacher will give you some pictures of different objects.
Draw and label each circle.
Circle B, with a radius of 5 cm.
Pause here so your teacher can review your work.
Circle D, with a diameter that is equal to Circle B’s radius.
First of 4 images of circles in different shapes. Image 1, circles within circles.
Second of 4 images of circles in different shapes. Image 2, caterpillar made of 5 circles.
Third of 4 images of circles in different shapes. Image 3, 3 interlocking circles.
Fourth of 4 images of circles in different shapes. Image 4, 7 circles in the shape of a flower.
A circle consists of all of the points that are the same distance away from a particular point called the center of the circle.
A segment that connects the center with any point on the circle is called a radius. For example, segments , , , and are all radii of Circle 2. (We say one radius and two radii.) The length of any radius is always the same for a given circle. For this reason, people also refer to this distance as the radius of the circle.
Two circles labeled circle 1 and circle 2. Circle 1 has a center at P and the points A, C, F, B, D, and E lie on the circle. Diameters A B, C D, and E F are drawn. Circle 2 has a center at Q and the points G, H, I and J lie on the circle. Line segments Q G, Q H, Q I, and Q J are drawn.
A segment that connects two opposite points on a circle (passing through the circle’s center) is called a diameter. For example, segments , , and are all diameters of Circle 1. All diameters in a given circle have the same length because they are composed of two radii. For this reason, people also refer to the length of such a segment as the diameter of the circle.
The circumference of a circle is the distance around it. If a circle was made of a piece of string and we cut it and straightened it out, the circumference would be the length of that string. A circle always encloses a circular region. The region enclosed by Circle 2 is shaded, but the region enclosed by Circle 1 is not. When we refer to the area of a circle, we mean the area of the enclosed circular region.
A circle is made of all the points that are the same distance from a given point. That given point is the center of the circle.
Every point on this circle is 5 cm away from point .
The circumference of a circle is the distance around the circle. If a circle has radius units, its circumference is units.
For example, a circle has a radius of 3 inches. Its circumference is , or inches. This is about 18.85 inches.
A diameter is a line segment that goes from one point on a circle to another and passes through the center. The length of this segment is also called the diameter. Every diameter of a circle is the same length.
A radius is a line segment that goes from the center of a circle to any point on the circle. The length of this segment is also called the radius. Every radius of a circle is the same length.
For example, is the radius of this circle with center .