1.6

1
Name the polygon by the number of sides.
1. 6
2. 10
2
Name the polygon by the number of sides.
3. 5
4. What is a regular polygon?
3
Name the polygon by the number of sides.
5. What is the length of the diagonal of a square
withside length 6?
4
Identify and name polyhedra
EXAMPLE 1
Tell whether the solid is a polyhedron. If it is,
name the polyhedron and find the number of faces,
vertices, and edges.
5
Identify and name polyhedron
EXAMPLE 1
6
Identify and name polyhedron
EXAMPLE 1
7
for Example 1
GUIDED PRACTICE
Tell whether the solid is a polyhedron. If it is,
name the polyhedron and find the number of
faces, vertices, and edges.
8
for Example 1
GUIDED PRACTICE
9
for Example 1
GUIDED PRACTICE
10
Use Eulers Theorem in a real-world situation
EXAMPLE 2
House Construction
11
Use Eulers Theorem in a real-world situation
EXAMPLE 2
To find the number of vertices, notice that there
are 5 vertices around each pentagonal wall, and
there are no other vertices. So, the frame of the
house has 10 vertices.
12
Use Eulers Theorem with Platonic solids
EXAMPLE 3
13
EXAMPLE 4
Describe cross sections
Describe the shape formed by the intersection of
the plane and the cube.
SOLUTION
a. The cross section is a square.
b. The cross section is a rectangle.
14
EXAMPLE 4
Describe cross sections
15
for Examples 2, 3, and 4
GUIDED PRACTICE
4. Find the number of faces, vertices, and
edges of the regular dodecahedron on page 796.
Check your answer using Eulers Theorem.
SOLUTION
Counting on the diagram, the dodecahedron has 12
faces, 20 vertices, and 30 edges. Use Eulers
theorem to
16
for Examples 2, 3, and 4
GUIDED PRACTICE
Describe the shape formed by the intersection of
the plane and the solid.
17
for Examples 2, 3, and 4
GUIDED PRACTICE
18
for Examples 2, 3, and 4
GUIDED PRACTICE
19
Daily Homework Quiz

Determine whether the solid is a polyhedron. If
it is, name it.
20
Daily Homework Quiz

21
Daily Homework Quiz

22
Daily Homework Quiz

4. Find the number of faces, vertices, and
edges of each polyhedron in Exercises 13.
5. A plane intersects a cone, but does not
intersect the base of the cone. Describe the
possible cross sections.