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Geometry for School and Home
Activity 3.8
Assignment 3.9
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Assignment 8.15
Polyhedrons
Objectives
Name faces, edges, and vertices of polyhedrons.
Classify polygons.
Develop and apply Euler's theorem relating the number of faces, vertices, and edges of polyhedrons.
About Geometry Worksheet Assignment 8.15:
Assignment 8.15 is an introduction to polyhedrons and the development of a theorem about polyhedrons (Euler's Law).
Prerequisite Skills: Classify polygons (Assignment 3.3). Name polygons, vertices of polygons, and sides of polygons (Assignment 3.1).
Definitions: A polyhedron is a space figure made of polygons that enclose a single region.
Each polygon in a polyhedron is a face of the polyhedron.
An edge of a polyhedron is a common side of two faces.
A vertex of the polyhedron is a common vertex of three or more facres.
Theorem: Euler's Law: In a polyhedron, the sum of the number of faces and the number of vertices equal the sum of the number of edges and 2.
F + V = E + 2 (F is number of faces; V is number of vertices; E is number of edges)