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.

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.

Geometric objects are abstractions that seem to have a connection to real world objects.

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.

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 collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

This collection of clip art images includes image sequences for key topics in geometry. This includes points, lines, planes, angles, triangles, quadrilaterals, and polygons. Each sequence of images provides an overview of the topic.

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

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?