Three-Dimensional Solids Polyhedron – A solid with all flat surfaces that enclose a single region of space. Face – Each flat surface of the polyhedron.

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Presentation transcript:

Three-Dimensional Solids Polyhedron – A solid with all flat surfaces that enclose a single region of space. Face – Each flat surface of the polyhedron. All the faces are polygons. Edges – The line segments where the faces of the polyhedron intersect. Vertex – The point where the edges intersect.

Three-Dimensional Solids Prism – A polyhedron with two parallel congruent faces. Prisms are named by the shape of their bases. Bases – The two parallel congruent faces. The other faces of a prism are parallelograms. The intersection of three edges of a prism is a vertex. Regular Prism – A prism with bases that are regular polygons.

Example 1-2g a. Identify the solid. Name the bases, faces, edges, and vertices. Answer: triangular prism Bases: Faces: Edges: Vertices: A, B, C, E, F, G

Three-Dimensional Solids Pyramid – A polyhedron with all faces except one intersecting a vertex. Pyramids are named for their bases, which can be a polygon of any variety.

Example 1-2j c. Identify the solid. Name the bases, faces, edges, and vertices. Answer: pentagonal pyramid Bases: ABCDE Faces: Edges: Vertices: A, B, C, D, E, F

Three-Dimensional Solids Regular Polyhedron – A polyhedron with all of its faces that are regular congruent polygons and edges that are all congruent. Cross section – The intersection of a plane and a solid such that the plane is parallel to the base or bases of the solid.

Example 1-3c A solid cone is going to be sliced so that the resulting flat portion can be dipped in paint and used to make prints of different shapes. How should the cone be sliced to make prints of a circle, triangle, and an oval? Answer: If the cone were to be cut parallel to the base, the cross-section would be a circle.

Example 1-3d Answer: If the cone were to be cut perpendicular to the base, the slice would be a triangle. If the cone were to be cut on an angle to the base, the slice would be an oval.

Three-Dimensional Solids Cylinder – A solid with congruent circular bases in a pair of parallel planes. Cone – A solid with a circular base and a vertex. Sphere – A solid consisting of a set of all points in space that are a given distance from a fixed point.

Example 1-2i b. Identify the solid. Name the bases, faces, edges, and vertices. Answer: cylinder Bases: