1. Geometry Chapter 11
11-5: Exploring Solids

2. Exploring Solids
Objective: Students will be able to identify the key characteristics of various solids.
Agenda
Polyhedron
Non-Polyhedron

3. Polyhedron
A Polyhedron is a solid that is bounded by polygons, called faces.

4. 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.

5. 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.

6. 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:

7. 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

8. Polyhedron - Pyramid 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

9. 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

10. 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

11. 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

12. Example 1a
Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.

13. Example 1a Yes, the solid is a rectangular prism.
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

14. Example 1b
Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.

15. Example 1b Yes, the solid is a hexagonal pyramid.
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

16. Example 1c
Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.

17. Example 1c No, the solid is not a polyhedron. It is a cone.
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.

18. Example 1d
Tell whether the solid is a polyhedron. If its, name the polyhedron and state the number of faces, vertices, and edges it has.

19. Example 1d Yes, the solid is a triangular prism.
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

20. Regular Polyhedra
A polyhedron is regular if all of its faces are congruent regular polygons.

21. 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.

22. 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.

23. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.

24. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.
Regular Tetrahedron
4 Faces

25. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.
Cube
6 Faces

26. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.
Regular Octahedron
8 Faces

27. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.
Regular Dodecahedron
12 Faces

28. Regular Polyhedra
There are five regular Polyhedra, called Platonic Solids.
Regular Icosahedron
20 Faces