Geometry Chapter 11 11 5 EXPLORING SOLIDS Exploring
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Geometry Chapter 11 11 -5: EXPLORING SOLIDS
Exploring Solids Objective: Students will be able to identify the key characteristics of various solids. Agenda Polyhedron Non-Polyhedron
Polyhedron A Polyhedron is a solid that is bounded by polygons, called faces.
Polyhedron A Polyhedron is a solid that is bounded by polygons, called faces. An edge is a line segment formed by the intersection of two faces.
Polyhedron A Polyhedron is a solid that is bounded by polygons, called faces. An edge is a line segment formed by the intersection of two faces. A vertex of a Polyhedron is a point where three or more edges meet.
Polyhedron A Polyhedron is a solid that is bounded by polygons, called faces. An edge is a line segment formed by the intersection of two faces. A vertex of a Polyhedron is a point where three or more edges meet. Examples:
Polyhedron - Prism A Prism is a polyhedron with the following features: It has two bases that are congruent, parallel polygons. The sides are all parallelograms. Examples: Rectangular Prism Triangular Prism
Polyhedron - Pyramid A Pyramid is a polyhedron with the following features: It has a single base that is a polygon. The sides are all triangles. Examples: Polyhedron Pyramid Triangular Pyramid Pentagonal Pyramid
Non-Polyhedron - Cylinder A Cylinder is a non-polyhedron with the following features: It has two bases that are congruent, parallel circles. It has no sides; its edges are round. Cylinder
Non-Polyhedron - Cone A Cone is a non-polyhedron with the following features: It has a singe base, which is a circle. It has no sides; its edges are round. Cone
Non-Polyhedron - Sphere A Sphere is a non-polyhedron with the following features: It is a set of all points in space equidistant from a given point, called the center. It possess all the lines a circle does, such as radius, chord and diameter. Sphere
Example 1 a Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.
Example 1 a Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has. Yes, the solid is a rectangular prism. It has 6 faces, 8 vertices and 12 edges
Example 1 b Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.
Example 1 b Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has. Yes, the solid is a hexagonal pyramid. It has 7 faces, 7 vertices and 12 edges
Example 1 c Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.
Example 1 c Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has. No, the solid is not a polyhedron. It is a cone.
Example 1 d Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.
Example 1 d Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has. Yes, the solid is a triangular prism. It has 5 faces, 6 vertices, and 9 edges
Regular Polyhedra A polyhedron is regular if all of its faces are congruent regular polygons.
Regular Polyhedra A polyhedron is regular if all of its faces are congruent regular polygons. A polyhedron is convex if any two points on its surface can be connected by a segment in or on the polyhedron.
Regular Polyhedra A polyhedron is regular if all of its faces are congruent regular polygons. If this segment goes outside the polyhedron, then it is concave.
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids.
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids. Regular Tetrahedron 4 Faces
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids. Cube 6 Faces
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids. Regular Octahedron 8 Faces
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids. Regular Dodecahedron 12 Faces
Regular Polyhedra There are five regular Polyhedra, called Platonic Solids. Regular Icosahedron 20 Faces
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