Section 1
Definition of a Circle
Property
A circle is the set of all points in a plane that lie at a given distance, called the radius, from a fixed point called the center.
In this Grade 7 lesson from Illustrative Mathematics Chapter 3: Measuring Circles, students explore how to determine whether two measured quantities have a proportional relationship by plotting values on a coordinate plane and examining whether the points fall close to a line through the origin. Using squares as a hands-on context, students measure diagonal length alongside both perimeter and area, then compare how each relationship behaves graphically and numerically. The lesson builds foundational skills for recognizing and modeling proportional relationships from real measurement data.
Section 1
Definition of a Circle
A circle is the set of all points in a plane that lie at a given distance, called the radius, from a fixed point called the center.
Section 2
Relationship Between Radius and Diameter
The diameter () of a circle is twice its radius (). The radius is half of the diameter.
Section 3
Circumference of a Circle
The distance from the center of a circle to any point on the circle itself is called the radius of the circle.
The diameter of a circle is the length of a line segment joining two points on the circle and passing through the center. Thus, the diameter of a circle is twice its radius.
The perimeter of a circle is called its circumference.
The circumference of a circle is given by
where is the diameter of the circle. The Greek letter (pi) stands for an irrational number:
Circumference is the special name for a circle's perimeter. It's the distance around the circle's edge. This distance is always a little more than 3 times the circle's diameter, a constant ratio we call pi ().
Expand to review the lesson summary and core properties.
Section 1
Definition of a Circle
A circle is the set of all points in a plane that lie at a given distance, called the radius, from a fixed point called the center.
Section 2
Relationship Between Radius and Diameter
The diameter () of a circle is twice its radius (). The radius is half of the diameter.
Section 3
Circumference of a Circle
The distance from the center of a circle to any point on the circle itself is called the radius of the circle.
The diameter of a circle is the length of a line segment joining two points on the circle and passing through the center. Thus, the diameter of a circle is twice its radius.
The perimeter of a circle is called its circumference.
The circumference of a circle is given by
where is the diameter of the circle. The Greek letter (pi) stands for an irrational number:
Circumference is the special name for a circle's perimeter. It's the distance around the circle's edge. This distance is always a little more than 3 times the circle's diameter, a constant ratio we call pi ().