Upload
percival-spencer
View
217
Download
4
Tags:
Embed Size (px)
Citation preview
1
Geometry Section 6-3B Geometry Section 6-3B
Regular PolyhedronsRegular Polyhedrons
Page 448Page 448
If you have your solids, you If you have your solids, you might like to use them today.might like to use them today.Test Friday – Shapes on FridayTest Friday – Shapes on Friday
2
Regular Polyhedrons:Regular Polyhedrons:A regular polyhedron has:
Congruent edges and faces
Faces that are regular polygons
An equal number of edges meeting at each vertexPg.448
5 regular polyhedrons – let’s take a look.
A convex regular polyhedron is one with no “dents”.
3
Regular Polyhedron:Regular Polyhedron:There are only 5 convex regular polyhedrons.
They were discovered over 2000 years ago and are name the Platonic Solids in honor of the Greek philosopher Plato.
Pg.448
4
Explore: Explore: (fill in your chart)(fill in your chart)
Tetrahedron
Pg.449
The faces are triangles
4 faces
4 vertices
6 edges
THINK: If each triangle is regular, what is the measure of each angle? 60o
So what is the sum of the measures of the angles that meet at each vertex? 180o
5
Explore: Explore: (fill in your chart)(fill in your chart)
Hexahedron
Pg.449
The faces are squares
6 faces
8 vertices
12 edges
What is the sum of the measures of the angles that meet at each vertex? 270o
6
Explore: Explore: (fill in your chart)(fill in your chart)
Octahedron
Pg.449
The faces are triangles
8 faces
6 vertices
12 edges
What is the sum of the measures of the angles that meet at each vertex? 240o
7
Explore: Explore: (fill in your chart)(fill in your chart)
Dodecahedron
Pg.449
The faces are pentagons
12 faces
20 vertices
30 edges
What is the sum of the measures of the angles that meet at each vertex? 324o
8
Explore: Explore: (fill in your chart)(fill in your chart)
Icosahedron
Pg.449
The faces are triangles
20 faces
12 vertices
30 edges
What is the sum of the measures of the angles that meet at each vertex? 300o
9
Exercises:Exercises:
#1-5
Pg.450
Classify each regular polyhedron.
1. tetraheadron2. octahedron 3. hexahedron 4. dodecahedron 5. icosahedron
10
Exercises:Exercises:
#6-7
Pg.450
Name the convex regular polyhedron that has the given set of characteristics.
6. Four equilateral triangles meeting at each vertex.
octahedron
dodecahedron
7. Pentagonal faces
11
Exercises:Exercises:
#12
Pg.450
If a platonic solid is randomly selected from the 5 possibilities, what is the probability that the solid
will have:
a. triangular faces 35
b. square faces 15
c. pentagonal faces 15
12
Exercises:Exercises:
#14-15
Pg.450
Find the sum of the face angles at each vertex of a:
14. regular octahedron 240o
15. regular dodecahedron 324o
13
Homework: Practice 6-3B
Test Friday
Solids due Friday