This hands-on activity is a companion to the video segment from the Geometry Applications: Angles and Planes video. In particular, it supports the segment on the architecture of Himeji Castle.

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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The definition of the term "3-4-5 Right Triangle."

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The definition of the term "30-60-90 Right Triangles."

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The definition of the term "45-45-90 Right Triangles."

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The definition of the term "5-12-13 Right Triangle."

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The definition of the term "Acute Angle."

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The definition of the term "Complementary Angle."

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The definition of the term "Legs of a Right Triangle."

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The definition of the term "Line."

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The definition of the term "Line Segment."

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The definition of the term "Midpoint."

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The definition of the term "Obtuse Angle."

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The definition of the term "Point."

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The definition of the term "Ray."

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The definition of the term "Reflex Angle."

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The definition of the term "Right Angle."

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