 # Geometric Solids A three dimensional figure that has three dimensions: length, width, and height. cylinder Rectangular prism cube pyramid cone.

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Geometric Solids A three dimensional figure that has three dimensions: length, width, and height. cylinder Rectangular prism cube pyramid cone

Polyhedron: A 3-D figure whose faces are all polygons.
Some Vocabulary Polyhedron: A 3-D figure whose faces are all polygons. Base: The face that is used to name a polyhedron.

Step 2: Determine if the object is a prism or pyramid.
Naming Polyhedrons Step 1: Identify the base of the solid. It will be used to name the polyhedron. Hint: It will be the name of a polygon. Step 2: Determine if the object is a prism or pyramid. Step 3: Name the polyhedron.

Naming Solids: Step 1 Identify the base of the solid. It will be used to name the polyhedron. Hint: It will be the name of a polygon. Example: There is one base, and it is a pentagon.

Determine if the object is a prism or pyramid.
Naming Solids: Step 2 Determine if the object is a prism or pyramid.

Naming Solids: Step 2 Example:
There is one base that is a polygon and there are five triangular faces, which makes it a pyramid.

Naming Solids: Step 3 Name the polyhedron
Combine what you found in Steps 1 and 2 to name the figure. Example: Base: Pentagon Faces: Pyramid Name: Pentagonal Pyramid

Not Polyhedrons Other three-dimensional figures include cylinders, cones, and spheres. These figures are not polyhedrons because they are not made of faces that are all polygons. Cylinders Cones Spheres

Cross Sections Video

Let’s Review Review geometric figures: right rectangular prism, plane. Coach’s Commentary Proper use of vocabulary is essential as students move to higher levels of mathematics.

Vocabulary: Cross section
The two-dimensional shape that results from cutting a three-dimensional shape with a plane Core Lesson Imagine the surface of the water in a cylindrical drinking glass. When we look at it from the side, the cross section appears to be an oval, but if we look at it straight on, we can see that the cross section of a cylinder is a circle. We can imagine cross sections of right rectangular prisms in a similar way. Coach’s Commentary A familiar situation such as this can help students move to more complex images.

Core Lesson If we were to cut a right rectangular prism with a plane parallel to its base, what would be the shape of the resulting cross section? Observe how the plane moves across the prism and try to imagine the resulting cross section. Notice the blue shaded region – this is the cross section. From this perspective, it looks like a parallelogram, but if we stand it up and look at it straight on, we can see that it is a rectangle. Coach’s Commentary This series of animations was designed to help students visualize the “cutting” process step by step.

Core Lesson Now let’s consider a plane that is perpendicular to the base and parallel to the front face of the prism. What shape do you think this cross section will have? Again we see the plane intersecting with the prism. Can you visualize the cross section? Now we can see the cross section in blue. This cross section is also a rectangle.

Core Lesson If we were to cut a right rectangular pyramid with a plane parallel to its base, what would be the shape of the resulting cross section? Observe how the plane moves across the pyramid and try to imagine the resulting cross section. Notice the blue shaded region – this is the cross section. From this perspective, it looks like a parallelogram, but if we stand it up and look at it straight on, we can see that it is a rectangle. Coach’s Commentary This series of animations was designed to help students visualize the “cutting” process step by step.

Core Lesson Now let’s consider a plane that is perpendicular to the base of the pyramid and contains its vertex. The vertex is the point where the triangular faces intersect. What shape do you think this cross section will have? Again we see the plane intersecting with the pyramid. Can you visualize the cross section? Now we can see the cross section in blue, and conclude that it is a triangle.

Practice!

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