Classify three-dimensional figures according to their properties. Use nets and cross sections to analyze three-dimensional figures. Extend midpoint and distance formulas to three dimensions

1. Obj. 49 Solid Geometry
The student is able to (I can):
• Classify three-dimensional figures according to their
properties.
• Use nets and cross sections to analyze three-dimensional
figures.
• Extend midpoint and distance formulas to three
dimensions

2. face
edge
vertex
The flat surface on a three-dimensional
figure.
The segment that is the intersection of
two faces.
The point that is the intersection of three
or more edges.
face
edge
vertex•

3. prism
cylinder
Two parallel congruent polygon bases
connected by faces that are
parallelograms.
Two parallel congruent circular bases and a
curved surface that connects the bases.

4. pyramid
cone
A polygonal base with triangular faces that
meet at a common vertex.
A circular base and a curved surface that
connects the base to a vertex.

5. A cube is a prism with six square faces.
Other prisms and pyramids are named
for the shape of their bases.

6. net A diagram of the surfaces of a three-
dimensional figure that can be folded to
form the figure.
To identify a figure from a net, look at the
number of faces and the shape of each
face.
This is the net of
a cube because it
has six squares.

7. Examples Describe the three-dimensional figure from
the net.
1.
2.
Triangular
Pyramid
Cylinder

8. cross section The intersection of a three-dimensional
figure and a plane.

9. Examples Describe the cross sections:
1.
2.
A hexagon
A triangle

10. The Platonic solids are made up of regular polygons.
Name
# of
faces
Polygon Picture
Tetrahedron 4
Equilateral
triangles
Octahedron 8
Equilateral
triangles
Icosahedron 20
Equilateral
triangles
Hexahedron
(cube)
6 Squares
Dodecahedron 12 Pentagons

11. Euler’s
Formula
For any polyhedron with V vertices, E edges,
and F faces, V − E + F = 2.
Example: If a given polyhedron has 12
vertices and 18 edges, how many faces
does it have?
− + =
− + =
=
V E F 2
12 18 F 2
F 8

12. To find the length of d,
or
(Pyth. Theorem)
w
h
x
d
+ =
+ =
2 2 2
2 2 2
w x
h x d
+ + =2 2 2 2
w h d
= + +2 2 2
d w h

13. Examples
(round to the
nearest tenth)
1. Find the length of the diagonal of a 3
in. by 4 in. by 5 in. rectangular prism.
2. Find the height of a rectangular prism
with an 8 ft by 12 ft base and an 18 ft
diagonal.
= + +
= ≈
2 2 2
d 3 4 5
50 7.1 in.
= + +
= +
=
= ≈
2 2 2 2
2
2
18 8 12 h
324 208 h
h 116
h 116 10.8 ft.

14. space The set of point in all three dimensions.
Instead of two coordinates, we need three
coordinates to locate a point in space, so
we now have an x-axis, a y-axis, and a z-
axis.
Example: Plot the point (3, 2, 4)

15. Example: Find the distance and midpoint between (6, 11, 3)
and (4, 6, 12). Round to the nearest tenth if necessary.
( ) ( ) ( )= − + − + −
= + + = ≈
2 2 2
d 4 2 6 11 12 3
4 25 81 110 10.5
( )
+ + + 
 
 
6 4 11 6 3 12
M , ,
2 2 2
M 5, 8.5, 7.5