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.

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.

Himeji castle in Japan is a marvel of architecture and a startling example of geometry and military science.

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.

This cheat sheet gathers together the resources on the topic of parallel and perpendicular lines. See the descriptions and links below. Each link takes you to a collection of resources around that topic. The middle column indicates the number of resources available and the third column takes you to page on Media4Math where those resources can be found.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to Angles. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to Angles. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.

This is a collection of definitions related to angles and related concepts. This includes general definitions for angles, angle measures, and angle properties, as well as specific angle types. Relationships among different types of angles are also defined.