The Geometry of Solids Section 10.1.

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Presentation transcript:

The Geometry of Solids Section 10.1

A solid formed by polygons enclosing a region is called a polyhedron. The flat surface (or polygon) are called a face. The segment where two faces (or polygons) meet is called an edge. The point of intersection of three edges is called a vertex.

Just as we classify polygons by the number of sides, we classify polyhedron by their number of faces.

A regular polyhedron is a three dimensional figure where each face of a polyhedron is a regular polygon Each face is congruent to each other face Each face meets other faces exactly the same way at all times

Prisms A prism is a special type of polyhedron Has two congruent bases Bases are parallel The other faces of the prism are called lateral faces and may be a different polygon from the base.

Right and Oblique Prisms If a prism’s lateral faces are rectangles, then the prism is called a right prism. The altitude of a prism is any perpendicular segment from one base to the other. A prism that is not a right prism is called an oblique prism.

Pyramids A pyramid is another special polyhedron. Pyramids have just one base that is any polygon. The other faces are called lateral faces. The common vertex where the lateral faces meet is the vertex of the pyramid. The altitude is a perpendicular segment from the vertex to the base.

Other Geometric Solids One solid with a curved surface is a cylinder. A cylinder, like a prism, has two congruent, parallel bases (circles). If a segment were drawn between the centers of the two circular bases of a right cylinder it would be called an altitude. The radius of a cylinder is a radius of the base.

Cones A cone is another type of geometric solid with a curved surface. The base is a circle. The altitude is a perpendicular line segment from the vertex to the base.

Spheres A final type of solid with curved surfaces is a sphere. A sphere is the set of all points equidistant from a given point in space. The radius is the given distance.

On an oblique cylinder the altitude would be a perpendicular line segment between the two bases.