Illustrative Math Alignment: Grade 7 Unit 3

Measuring Circles

Lesson 1: How Well Can You Measure?

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Definition--Geometry Basics--Central Angle	Central Angle Topic Geometry Basics Definition An angle whose vertex is the center of a circle and whose sides are radii. Description A central angle is an angle whose vertex is at the center of a circle and whose sides are radii of the circle. This concept is essential in understanding the properties of circles and the relationships between angles and arcs. For example, the measure of a central angle is equal to the measure of the arc it intercepts. Understanding central angles is important for solving problems related to circle geometry and trigonometry.	Definition of a Circle
Definition--Geometry Basics--Central Angle	Central Angle Topic Geometry Basics Definition An angle whose vertex is the center of a circle and whose sides are radii. Description A central angle is an angle whose vertex is at the center of a circle and whose sides are radii of the circle. This concept is essential in understanding the properties of circles and the relationships between angles and arcs. For example, the measure of a central angle is equal to the measure of the arc it intercepts. Understanding central angles is important for solving problems related to circle geometry and trigonometry.	Definition of a Circle
Definition--Geometry Basics--Central Angle	Central Angle Topic Geometry Basics Definition An angle whose vertex is the center of a circle and whose sides are radii. Description A central angle is an angle whose vertex is at the center of a circle and whose sides are radii of the circle. This concept is essential in understanding the properties of circles and the relationships between angles and arcs. For example, the measure of a central angle is equal to the measure of the arc it intercepts. Understanding central angles is important for solving problems related to circle geometry and trigonometry.	Definition of a Circle
Definition--Circle Concepts--Chord	Chord Topic Circles Definition A chord is a line segment with both endpoints on the circle.	Definition of a Circle
Definition--Circle Concepts--Chord	Chord Topic Circles Definition A chord is a line segment with both endpoints on the circle.	Definition of a Circle
Definition--Circle Concepts--Chord	Chord Topic Circles Definition A chord is a line segment with both endpoints on the circle.	Definition of a Circle
Definition--Circle Concepts--Circle	Circle Topic Circles Definition A circle is a set of all points in a plane equidistant from a given point, the center. Description The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is (x − h)2 + (y − k)2 = r2	Definition of a Circle
Definition--Circle Concepts--Circle	Circle Topic Circles Definition A circle is a set of all points in a plane equidistant from a given point, the center. Description The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is (x − h)2 + (y − k)2 = r2	Definition of a Circle
Definition--Circle Concepts--Circle	Circle Topic Circles Definition A circle is a set of all points in a plane equidistant from a given point, the center. Description The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is (x − h)2 + (y − k)2 = r2	Definition of a Circle
Definition--Circle Concepts--Diameter	Diameter Topic Circles Definition The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle, calculated as D = 2πr. Description The diameter is a fundamental concept in geometry, representing the longest distance across a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula D = 2πr	Definition of a Circle
Definition--Circle Concepts--Diameter	Diameter Topic Circles Definition The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle, calculated as D = 2πr. Description The diameter is a fundamental concept in geometry, representing the longest distance across a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula D = 2πr	Definition of a Circle
Definition--Circle Concepts--Diameter	Diameter Topic Circles Definition The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle, calculated as D = 2πr. Description The diameter is a fundamental concept in geometry, representing the longest distance across a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula D = 2πr	Definition of a Circle
Definition--Circle Concepts--Radius of a Circle	Radius of a Circle Topic Circles Definition The radius of a circle is a line segment from the center to any point on the circle.	Definition of a Circle
Definition--Circle Concepts--Radius of a Circle	Radius of a Circle Topic Circles Definition The radius of a circle is a line segment from the center to any point on the circle.	Definition of a Circle
Definition--Circle Concepts--Radius of a Circle	Radius of a Circle Topic Circles Definition The radius of a circle is a line segment from the center to any point on the circle.	Definition of a Circle
Definition--Circle Concepts--Secant to a Circle	Secant to a Circle Topic Circles Definition A secant is a line that intersects a circle at two points. Description Secants are significant in geometry, representing lines that intersect a circle at two distinct points. These lines are used in various applications, such as in design and architecture, where precise measurements of angles and distances are essential. In mathematics, secants are explored in the context of circle theorems, providing insights into the properties of lines and circles. In education, understanding secants helps students develop geometric reasoning and problem-solving skills, which are essential for advanced studies in geometry and trigonometry.	Definition of a Circle
Definition--Circle Concepts--Secant to a Circle	Secant to a Circle Topic Circles Definition A secant is a line that intersects a circle at two points. Description Secants are significant in geometry, representing lines that intersect a circle at two distinct points. These lines are used in various applications, such as in design and architecture, where precise measurements of angles and distances are essential. In mathematics, secants are explored in the context of circle theorems, providing insights into the properties of lines and circles. In education, understanding secants helps students develop geometric reasoning and problem-solving skills, which are essential for advanced studies in geometry and trigonometry.	Definition of a Circle
Definition--Circle Concepts--Secant to a Circle	Secant to a Circle Topic Circles Definition A secant is a line that intersects a circle at two points. Description Secants are significant in geometry, representing lines that intersect a circle at two distinct points. These lines are used in various applications, such as in design and architecture, where precise measurements of angles and distances are essential. In mathematics, secants are explored in the context of circle theorems, providing insights into the properties of lines and circles. In education, understanding secants helps students develop geometric reasoning and problem-solving skills, which are essential for advanced studies in geometry and trigonometry.	Definition of a Circle
Definition--Circle Concepts--Sector	Sector Topic Circles Definition A sector is a portion of a circle enclosed by two radii and the arc between them. Description Sectors are fundamental in the study of circles, representing a portion of the circle's area. These shapes are used in various applications, such as in design and architecture, where precise measurements of angles and areas are essential. The area of a sector is calculated using the formula A = 1/2r2θ	Definition of a Circle
Definition--Circle Concepts--Sector	Sector Topic Circles Definition A sector is a portion of a circle enclosed by two radii and the arc between them. Description Sectors are fundamental in the study of circles, representing a portion of the circle's area. These shapes are used in various applications, such as in design and architecture, where precise measurements of angles and areas are essential. The area of a sector is calculated using the formula A = 1/2r2θ	Definition of a Circle
Definition--Circle Concepts--Sector	Sector Topic Circles Definition A sector is a portion of a circle enclosed by two radii and the arc between them. Description Sectors are fundamental in the study of circles, representing a portion of the circle's area. These shapes are used in various applications, such as in design and architecture, where precise measurements of angles and areas are essential. The area of a sector is calculated using the formula A = 1/2r2θ	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle	Math Clip Art--Circle Illustrations--Circle Topic Geometry Concepts Description This clip art illustrates a basic circle, which is a fundamental shape in geometry. A circle is defined as the set of all points in a plane that are equidistant from a central point. This image serves as a visual representation of this concept, showcasing the perfect symmetry and continuous curvature that characterize circles.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle	Math Clip Art--Circle Illustrations--Circle Topic Geometry Concepts Description This clip art illustrates a basic circle, which is a fundamental shape in geometry. A circle is defined as the set of all points in a plane that are equidistant from a central point. This image serves as a visual representation of this concept, showcasing the perfect symmetry and continuous curvature that characterize circles.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Topic Geometry Concepts Description This clip art depicts a circle centered at the origin (0,0) of a coordinate grid. It illustrates the relationship between circles and the Cartesian coordinate system, a fundamental concept in analytic geometry. The image shows how a circle's position can be defined in relation to the x and y axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Topic Geometry Concepts Description This clip art depicts a circle centered at the origin (0,0) of a coordinate grid. It illustrates the relationship between circles and the Cartesian coordinate system, a fundamental concept in analytic geometry. The image shows how a circle's position can be defined in relation to the x and y axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Topic Geometry Concepts Description This clip art depicts a circle centered at the origin (0,0) of a coordinate grid. It illustrates the relationship between circles and the Cartesian coordinate system, a fundamental concept in analytic geometry. The image shows how a circle's position can be defined in relation to the x and y axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Topic Geometry Concepts Description This clip art depicts a circle centered at the origin (0,0) of a coordinate grid. It illustrates the relationship between circles and the Cartesian coordinate system, a fundamental concept in analytic geometry. The image shows how a circle's position can be defined in relation to the x and y axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Topic Geometry Concepts Description This clip art shows a circle centered at the origin of a coordinate grid with its radius clearly labeled. This illustration is crucial for understanding the relationship between a circle's radius and its equation in the coordinate plane. The labeled radius helps visualize how the distance from the center to any point on the circle remains constant, which is the defining property of a circle.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Topic Geometry Concepts Description This clip art shows a circle centered at the origin of a coordinate grid with its radius clearly labeled. This illustration is crucial for understanding the relationship between a circle's radius and its equation in the coordinate plane. The labeled radius helps visualize how the distance from the center to any point on the circle remains constant, which is the defining property of a circle.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Topic Geometry Concepts Description This clip art shows a circle centered at the origin of a coordinate grid with its radius clearly labeled. This illustration is crucial for understanding the relationship between a circle's radius and its equation in the coordinate plane. The labeled radius helps visualize how the distance from the center to any point on the circle remains constant, which is the defining property of a circle.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled	Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Topic Geometry Concepts Description This clip art shows a circle centered at the origin of a coordinate grid with its radius clearly labeled. This illustration is crucial for understanding the relationship between a circle's radius and its equation in the coordinate plane. The labeled radius helps visualize how the distance from the center to any point on the circle remains constant, which is the defining property of a circle.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1	Math Clip Art--Circle Illustrations--Circle Centered in Q1 Topic Geometry Concepts Description This clip art illustrates a circle centered in the first quadrant (Q1) of the coordinate plane. This representation is crucial for understanding how the position of a circle's center affects its equation and properties. In Q1, both x and y coordinates of the center are positive, which influences the circle's equation and its intersection with the axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1	Math Clip Art--Circle Illustrations--Circle Centered in Q1 Topic Geometry Concepts Description This clip art illustrates a circle centered in the first quadrant (Q1) of the coordinate plane. This representation is crucial for understanding how the position of a circle's center affects its equation and properties. In Q1, both x and y coordinates of the center are positive, which influences the circle's equation and its intersection with the axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1	Math Clip Art--Circle Illustrations--Circle Centered in Q1 Topic Geometry Concepts Description This clip art illustrates a circle centered in the first quadrant (Q1) of the coordinate plane. This representation is crucial for understanding how the position of a circle's center affects its equation and properties. In Q1, both x and y coordinates of the center are positive, which influences the circle's equation and its intersection with the axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1	Math Clip Art--Circle Illustrations--Circle Centered in Q1 Topic Geometry Concepts Description This clip art illustrates a circle centered in the first quadrant (Q1) of the coordinate plane. This representation is crucial for understanding how the position of a circle's center affects its equation and properties. In Q1, both x and y coordinates of the center are positive, which influences the circle's equation and its intersection with the axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2	Math Clip Art--Circle Illustrations--Circle Centered in Q2 Topic Geometry Concepts Description This clip art shows a circle centered in the second quadrant (Q2) of the coordinate plane. In Q2, the x-coordinate of the center is negative while the y-coordinate is positive. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2	Math Clip Art--Circle Illustrations--Circle Centered in Q2 Topic Geometry Concepts Description This clip art shows a circle centered in the second quadrant (Q2) of the coordinate plane. In Q2, the x-coordinate of the center is negative while the y-coordinate is positive. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2	Math Clip Art--Circle Illustrations--Circle Centered in Q2 Topic Geometry Concepts Description This clip art shows a circle centered in the second quadrant (Q2) of the coordinate plane. In Q2, the x-coordinate of the center is negative while the y-coordinate is positive. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2	Math Clip Art--Circle Illustrations--Circle Centered in Q2 Topic Geometry Concepts Description This clip art shows a circle centered in the second quadrant (Q2) of the coordinate plane. In Q2, the x-coordinate of the center is negative while the y-coordinate is positive. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3	Math Clip Art--Circle Illustrations--Circle Centered in Q3 Topic Geometry Concepts Description This clip art depicts a circle centered in the third quadrant (Q3) of the coordinate plane. In Q3, both the x and y coordinates of the center are negative. This positioning is essential for understanding how the location of a circle's center influences its equation and its interactions with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3	Math Clip Art--Circle Illustrations--Circle Centered in Q3 Topic Geometry Concepts Description This clip art depicts a circle centered in the third quadrant (Q3) of the coordinate plane. In Q3, both the x and y coordinates of the center are negative. This positioning is essential for understanding how the location of a circle's center influences its equation and its interactions with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3	Math Clip Art--Circle Illustrations--Circle Centered in Q3 Topic Geometry Concepts Description This clip art depicts a circle centered in the third quadrant (Q3) of the coordinate plane. In Q3, both the x and y coordinates of the center are negative. This positioning is essential for understanding how the location of a circle's center influences its equation and its interactions with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3	Math Clip Art--Circle Illustrations--Circle Centered in Q3 Topic Geometry Concepts Description This clip art depicts a circle centered in the third quadrant (Q3) of the coordinate plane. In Q3, both the x and y coordinates of the center are negative. This positioning is essential for understanding how the location of a circle's center influences its equation and its interactions with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4	Topic Geometry Concepts Description This clip art illustrates a circle centered in the fourth quadrant (Q4) of the coordinate plane. In Q4, the x-coordinate of the center is positive while the y-coordinate is negative. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4	Topic Geometry Concepts Description This clip art illustrates a circle centered in the fourth quadrant (Q4) of the coordinate plane. In Q4, the x-coordinate of the center is positive while the y-coordinate is negative. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4	Topic Geometry Concepts Description This clip art illustrates a circle centered in the fourth quadrant (Q4) of the coordinate plane. In Q4, the x-coordinate of the center is positive while the y-coordinate is negative. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4	Topic Geometry Concepts Description This clip art illustrates a circle centered in the fourth quadrant (Q4) of the coordinate plane. In Q4, the x-coordinate of the center is positive while the y-coordinate is negative. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.	Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle	Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.	Definition of a Circle and Applications of Coordinate Geometry
Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle	Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.	Definition of a Circle and Applications of Coordinate Geometry
Video Transcript: Geometry Applications: Circles	Video Transcript: Geometry Applications: Circles This is the transcript for the video of same title. Video contents: In this program we explore the properties of circles. We do this in the context of two real-world applications. In the first, we look at the design of the Roman Coliseum and explore how circular shapes could have been used to design this elliptical structure. In the second application we look at the Roman Pantheon, specifically its spherical dome, to see how the properties of chords and secants help clarify its unique design.	Applications of Circles