In this program we explore the properties of angles and planes. We do this in the context of two real-world applications. In the first, we explore Japan's Himeji Castle and in the process learn about different types of angles and how they're used in a defensive fortification. In the second applicaiton we explore sedimentary rock layers as examples of parallel planes. We explore the Burgess Shale fossils.

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The observatory in Arecibo, Puerto Rico provides astronomers insights into the structure of our solar system. Geometrically, the solar system relies on the plane known as the ecliptic. In studying the Earth’s orbit it is important to know that the Earth’s axis of rotation is at an angle relative to the ecliptic. This segment introduces the key themes of the program.

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Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science. The castle was used to protect samurai armies from invading forces, and the use of acute, obtuse, and right angles as part of the defense structure provide many opportunities for exploring the nature of geometric angles.

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In the Canadian Rockies, the Burgess Shale fossils provide a window to prehistoric Earth. Fossil layers are folded into sedimentary rocks. And sedimentary rocks are examples of parallel planes. This segment uses the properties of planes to analyze fossils.

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In this program we explore the properties of points and lines. We do this in the context of two real-world applications. In the first, we go to CERN and learn about the Large Hadron Collidor. We look at how points can represent particle positions in space and look at properties of points and lines. In the second application we investigate the properties of lines in the context of city grids.

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Geometric objects are abstractions that seem to have a connection to real world objects. In the case of a geometric point, we visit the CERN particle accelerator in Switzerland, where the smallest known subatomic particles are produced, to see how subatomic particles compare to geometric points. A mathematical analysis reveals the nature of geometric points and point-like materials objects.

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Many cities are laid out in a rectangular grid and are examples of intersecting lines and rays. We visit the city of Houston to investigate the geometric nature of the city grid in its downtown area. We explore properties of intersecting and parallel lines and why this is the most efficient way to organize a city or community.

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The definition of the term "Acute Angle."

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Definition of the term "Conditional Statement." Note: the download is a PNG file.

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Definition of the term "Center."

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The definition of the term "Chord."

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The definition of the term "Circle."

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

Definition of the term "Conditional Statement."

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

The definition of the term "Congruence."

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Definition of the term "Conditional Statement."

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Definition of the term "Contrapositive Statement."

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Definition of the term "Converse Statement."

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Definition of the term "Inverse Statement."

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The definition of the term "Line."

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

The definition of the term "Line Segment."

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The definition of the term "Parallel Lines."

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The definition of the term "Perpendicular Lines."

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

The definition of the term "Point."

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

This is the Teacher's Guide that accompanies Geometry Applications: Angles and Planes.

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

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

In this program we explore the properties of angles and planes. We do this in the context of two real-world applications. In the first, we explore Japan's Himeji Castle and in the process learn about different types of angles and how they're used in a defensive fortification. In the second applicaiton we explore sedimentary rock layers as examples of parallel planes. We explore the Burgess Shale fossils.

This video includes a video transcript: https://www.media4math.com/library/video-transcript-geometry-applications-angles-and-planes.

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