Illustrative Math Alignment: Grade 7 Unit 3

Topic

Circles

Definition

The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.

Topic

Circles

Definition

A tangent line is a straight line that touches a circle at exactly one point.

The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs.

The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs.

The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens.

We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens.

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.

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.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Circumscribing a Circle about a Triangle.

To see the complete collection of video transcriptsy, click on this link.

In this TI Nspire tutorial, the Geometry window is used to circumscribe a circle about a triangle. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .

Topic

Triangles

Definition

A circle inscribed in a triangle is a circle that touches all three sides of the triangle from the inside.

Description

An inscribed circle in a triangle, also known as an incircle, is a circle that is tangent to all three sides of the triangle. The center of this circle is called the incenter, which is the point where the angle bisectors of the triangle intersect.

Topic

Triangles

Definition

A triangle inscribed in a circle is a triangle whose vertices all lie on the circumference of the circle.

Description

A triangle inscribed in a circle, also known as a circumtriangle, is a triangle whose vertices all lie on the circumference of the circle. The circle is called the circumcircle, and its center is the circumcenter of the triangle.

Topic

Polygon Concepts

Definition

An incircle is the largest circle that can be inscribed within a polygon, tangent to all of its sides.

Definition

A circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter, and its radius is called the circumradius.

In this TI-Nspire Activity, use the Geometry and Graphing Tools to explore the ratio of Circumference to Radius as a linear function. 

Note: The Preview is a Google Slide Show and the download is a PPT. Subscribers to Media4Math can download resources.

Topic

Circles

Definition

An inscribed circle in a triangle is tangent to each of the triangle's sides.

Topic

Circles

Definition

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect, equidistant from the vertices.

Topic

Circles

Definition

The incenter of a triangle is the point where the angle bisectors intersect, equidistant from the sides.

Topic

Circles

Definition

An inscribed angle is an angle formed by two chords in a circle that share an endpoint.

Topic

Circles

Definition

A hexagon inscribed in a circle is a six-sided polygon where each vertex touches the circle.

Topic

Circles

Definition

A square inscribed in a circle has its vertices touching the circle.

Topic

Circles

Definition

A triangle inscribed in a circle has its vertices on the circle.

Topic

Circles

Definition

The point of tangency is the point where a tangent line touches the circle.

Topic

Circles

Definition

Concentric circles are circles that share the same center but have different radii.

Topic

Circles

Definition

Tangent circles are two or more circles that intersect at exactly one point.

Topic

Circles

Definition

Circles on a coordinate plane are defined by their center coordinates and radius.

Description

Understanding circles on a coordinate plane is essential for analyzing geometric shapes in a mathematical context. This concept is widely used in computer graphics, navigation systems, and physics simulations, where precise positioning and movement of circular objects are required. The standard equation of a circle in the coordinate plane is 

(x − h)2 + (y − k)2 = r2

Topic

Circles

Definition

Circular cross-sections are the intersections of a plane with a solid that result in a circle.

Topic

Circles

Definition

The equation of a circle in a plane is (x − h)2 + (y − k)2 = r2, where (h , k) is the center and r is the radius.

Topic

Circles

Definition

The ratio of the circumference to the diameter of a circle is the constant π.

Topic

Circles

Definition

The circumference of a circle is the distance around the circle, calculated as C = 2πr.

Description

The circumference is a fundamental concept in geometry, representing the perimeter of a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula 

C = 2πr 

Topic

Circles

Definition

The area of a circle is the space contained within its circumference, calculated as 

A = πr2

Description

The area of a circle is a fundamental concept in geometry, representing the space enclosed by the circle's boundary. This concept is widely applicable in fields such as physics, engineering, and design, where understanding the area is crucial for tasks like calculating material quantities or designing circular components. The formula 

A = πr2 

Topic

Circles

Definition

Circular models are representations of circular phenomena using mathematical equations and diagrams.

Topic

Circles

Definition

Circular functions are trigonometric functions that relate angles to ratios of sides in a right triangle.

Topic

Circles

Definition

The unit circle is a circle with a radius of one, centered at the origin of the coordinate plane.

Topic

Circles

Definition

Circular composite figures are shapes that include circles or parts of circles combined with other geometric figures.

Topic

Circles

Definition

Circular numerical models use numerical methods to analyze and simulate circular phenomena.

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

December 2022. In this issue of Math in the News we look at the Orion rocket's return to Earth from its lunar mission. This provides an opportunity to explore different types of orbits. 

Note: The download is a PPT file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

In this tutorial, learn how to use the unit circle to generate trigonometric functions.

Topic

3D Geometry

Description

This animation demonstrates how rotating a circle around its diameter creates a sphere. It's a powerful visualization of how 2D shapes can generate 3D objects through rotation, illustrating a fundamental concept in solid geometry and calculus.

Using animated math clip art like this helps students understand the relationship between 2D and 3D shapes, as well as the concept of solids of revolution. It bridges the gap between abstract mathematical concepts and visual representations, making complex ideas more accessible and engaging for learners.

Teachers can use this animation to introduce or reinforce various mathematical concepts:

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.

This is a collection of clip art images that show an application of direction variations in the context of circles.