CCSS

These are the resources that support this Common Core Standard.

HSG.C.A.4

There are 32 resources.
Title Description Thumbnail Image Curriculum Topics

Circular Structures

In this lesson students will use their basic understanding of circles to learn how circular structures are built. The example shown is that of the Roman Colosseum. Students will construct an oval shape from circular arcs to simulate the elliptical shape of the Roman Colosseum.

For this lesson make sure that students have ready access to a compass, ruler, grid paper (graph paper with x-y axes marked is preferred), and pencil with an eraser. The first construction has students creating a teardrop shape from circular arcs that have overlapping points of tangency. This first construction sets up the more elaborate second construction.

Students then look at a real-world application of using circular arcs to approximate the elliptical shape of the Roman Colosseum in a highly engaging video. Students analyze the architecture of the Roman Colosseum and are then shown how to build a scale model of the interior of  the Colosseum.

This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes. 

Closed Captioned Video: Geometry Applications: Circles

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.

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

Other Closed Captioned Videos

To see the complete collection of Closed Captioned Videos, click on this Link

GeoApps--Circles00.jpg Applications of Circles, Definition of a Circle

Closed Captioned Video: Geometry Applications: Circles, Segment 1: The Basics of Circles.

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.

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

Other Closed Captioned Videos

To see the complete collection of Closed Captioned Videos, click on this Link

GeoApps--Circles01.jpg Applications of Circles, Definition of a Circle

Closed Captioned Video: Geometry Applications: Circles, Segment 2: Circles and 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.

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

Other Closed Captioned Videos

To see the complete collection of Closed Captioned Videos, click on this Link

GeoApps--Circles02.jpg Applications of Circles, Definition of a Circle

Closed Captioned Video: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles

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.

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

Other Closed Captioned Videos

To see the complete collection of Closed Captioned Videos, click on this Link

GeoApps--Circles03.jpg Applications of Circles, Definition of a Circle

Closed Captioned Video: TI-Nspire Mini-Tutorial: Circumscribing a Circle about a Triangle

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 video includes a Worksheet: https://www.media4math.com/library/worksheet-ti-nspire-mini-tutorial-circumscribing-circle-about-triangle

A Video Transcript is available for this tutorial at this Link

Note: The download is Media4Math's guide to closed captioned videos.

Other Closed Captioned Videos

To see the complete collection of Closed Captioned Videos, click on this Link.

NspireTutorial--CircumscribingTriangle.jpg Geometric Constructions with Triangles

Definition--Circle Inscribed In a Triangle

The definition of the term "A Circle Inscribed in a Triangle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--CircleInscribedInTriangle.png Definition of a Circle

Definition--Circumcenter of a Triangle

The definition of the term "Circumcenter of a Triangle."

Note: The download is a JPG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--Circumcenter.jpg Geometric Constructions with Triangles

Definition--Circumcenter of a Triangle

The definition of the term "Circumcenter of a Triangle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--CircumcenterOfTriangle.png Definition of a Circle

Definition--Circumscribed Angle

The definition of the term "Circumbscribed Angle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--CircumscribedAngle.png Definition of a Circle

Definition--Incenter of a Triangle

The definition of one of the term "Incenter of a Triangle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--IncenterOfTriangle.png Definition of a Circle

Definition--Inscribed Angle

The definition of the term "Inscribed Angle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--InscribedAngle.png Definition of a Circle

Definition--Inscribed Angle Theorem

The definition the Inscribed Angle Theorem.

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--InscribedAngleTheorem.png Definition of a Circle

Definition--Inscribed Hexagon

The definition of the term "A Hexagon Inscribed in a Circle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--InscribedHexagon.png Definition of a Circle

Definition--Inscribed Square

The definition of the term "A Square Inscribed in a Circle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--InscribedSquare.png Definition of a Circle

Definition--Inscribed Triangle

The definition of the term "A Triangle Inscribed in a Circle."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--InscribedTriangle.png Definition of a Circle

Definition--Tangent Line

The definition of the term "Tangent Line."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition--TangentLine.png Definition of a Circle

Definition-Circle Inscribed in a Square

The definition of the term "A Circle Inscribed in a Square."

Note: The download is a PNG file.

Related Resources

To see the complete collection of glossary terms in the Visual Glossary, click on this link: https://media4math.com/Visual-Glossary

Definition-CircleInscribed.png Definition of a Circle

Geometry Applications Teachers Guide: Circles

This is the Teacher's Guide that accompanies Geometry Applications: Circles.

To view the full video: https://www.media4math.com/library/geometry-applications-circles

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-circles

Applications of Circles

VIDEO: Geometry Applications: Circles

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 video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles

This video includes a Teacher's Guide: https://www.media4math.com/library/geometry-applications-teachers-guide-circles

Applications of Circles, Definition of a Circle

VIDEO: Geometry Applications: Circles, Segment 1: The Basics of Circles.

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-1-basics-circles

Applications of Circles, Definition of a Circle

VIDEO: Geometry Applications: Circles, Segment 2: Circles and 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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-2-circles-and-arcs

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-circles-1

Applications of Circles, Definition of a Circle

VIDEO: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles

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.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-3-chords-and-inscribed-angles

This video includes a Promethean Flipchart: https://www.media4math.com/library/promethean-flipchart-geometry-applications-circles-2

Applications of Circles, Definition of a Circle

Google Earth Voyager Story: The Geometry of Castles

During Medieval times, castles were fortresses, mini-cities where the royalty lived, and symbols of power. Most castles were tall, imposing structures. But why were they so tall? Was it just for symbolic reasons, to allow a king to show his center of power and influence? In this exploration, we will explore the geometry of castles in order to better understand why they were built the way they were. To see the Google Earth version of this lesson go to this link (best viewed in Chrome).

Note: The download is the Teacher's Guide.

To see the complete collection of Google Voyager Stories, click on this link

Applications of Angles and Planes

Promethean Flipchart: Geometry Applications: Circles 1

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Circles, Segment 2: Circles and Arcs]: https://www.media4math.com/library/geometry-applications-circles-segment-2-circles-and-arcs

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-2-circles-and-arcs

Applications of Circles