11-1 Space Figures and Cross Sections
Objectives
To recognize polyhedra and their parts
To visualize cross sections of space figures
Lesson Vocabulary
- polyhedron
- face
- edge
- vertex
- cross section
In the Solve It, you used two-dimensional nets to represent a three-dimensional object.
A polyhedron is a space figure, or three-dimensional figure, whose surfaces are polygons. Each polygon is a face of the polyhedron. An edge is a segment that is formed by the intersection of two faces. A vertex is a point where three or more edges intersect.
Essential Understanding You can analyze a three-dimensional figure by using the relationships among its vertices, edges, and faces.
Problem 1 Identifying Vertices, Edges, and Faces
Plan
Can you see the solid?
A dashed line indicates an edge that is hidden from view. This figure has one four-sided face and four triangular faces.
How many vertices, edges, and faces are in the polyhedron below? List them.
There are five vertices: D, E, F, G, and H.
There are eight edges:
There are five faces:
✓ Got It?
-
- How many vertices, edges, and faces are in the polyhedron below? List them.
-
Reasoning Is
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs