6-3A Geometry Section 6-3B Regular Polyhedrons Page 448 If you have your solids, you might like to use them today. Test Friday – Shapes on Friday On the homework worksheet, #12 is the same as the Example in the book (and the proof we work together in the notes) Change this to #16 in the Exercises. Also, add some grids to the backside to help with #11. 1 1

5 regular polyhedrons – let’s take a look. A regular polyhedron has: Congruent edges and faces Faces that are regular polygons Pg. 448 An equal number of edges meeting at each vertex A convex regular polyhedron is one with no “dents”. 5 regular polyhedrons – let’s take a look.

Regular Polyhedron: There are only 5 convex regular polyhedrons. Pg. 448 They were discovered over 2000 years ago and are name the Platonic Solids in honor of the Greek philosopher Plato.

Explore: (fill in your chart) Tetrahedron The faces are triangles 4 faces Pg. 449 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

Explore: (fill in your chart) Hexahedron The faces are squares Pg. 449 6 faces 8 vertices 12 edges What is the sum of the measures of the angles that meet at each vertex? 270o

Explore: (fill in your chart) Octahedron The faces are triangles Pg. 449 8 faces 6 vertices 12 edges What is the sum of the measures of the angles that meet at each vertex? 240o

Explore: (fill in your chart) Dodecahedron The faces are pentagons Pg. 449 12 faces 20 vertices 30 edges What is the sum of the measures of the angles that meet at each vertex? 324o

Explore: (fill in your chart) Icosahedron The faces are triangles Pg. 449 20 faces 12 vertices 30 edges What is the sum of the measures of the angles that meet at each vertex? 300o

Classify each regular polyhedron. Exercises: Classify each regular polyhedron. #1-5 Pg. 450 1. tetraheadron 2. octahedron 3. hexahedron 4. dodecahedron 5. icosahedron

Exercises: octahedron dodecahedron Name the convex regular polyhedron that has the given set of characteristics. 6. Four equilateral triangles meeting at each vertex. #6-7 Pg. 450 octahedron 7. Pentagonal faces dodecahedron

Exercises: If a platonic solid is randomly selected from the 5 possibilities, what is the probability that the solid will have: 3 5 a. triangular faces #12 Pg. 450 1 5 b. square faces 1 5 c. pentagonal faces

Find the sum of the face angles at each vertex of a: Exercises: Find the sum of the face angles at each vertex of a: 14. regular octahedron 240o #14-15 Pg. 450 15. regular dodecahedron 324o

Homework: Practice 6-3B Test Friday Solids due Friday