12-1 Three Dimensional Figures
Orthogonal Drawing:
* The different views drawn two-dimensional
of a three dimensional figure.
* The views will be: front, left, right, and top.
Top View
Left View
Right View
CornerView
View(Perspective
(Perspectiveview):
View):
Corner
** When
When you
you draw
draw aa view
view from
from the
the corner
corner of
of
the
object.
the object.
** Isometric
Isometric dot
dot paper
paper can
can help
help with
with the
the
drawing of
of these
these views.
views. (Paper
drawing
(Paper with
with dots
dots
evenly spaced.)
spaced.)
evenly
Front View
(Views of a square pyramid.)
Top View:
* Will help you see how many sections are
belonging to the figure.
Front View:
* Will indicate which side (left or right) is
taller.
Side View:
* Will indicate what the different heights of
the figure will be.
Dark Segments indicate breaks in the
surface (example: different heights).
Making a model with blocks will help you in
drawing the corner view.
1.
Top View
Left View
Front View
Right View
a. Draw the back view of a figure given its
orthogonal drawing.
Polyhedron:
*A solid with flat surfaces that encloses a
single region of space.
Face:
* Each of the flat surfaces.
* Shape will be a polygon.
Prism:
* A polyhedron with 2 parallel congruent
faces. (These are called bases.)
* All other faces are parallelogram shape.
* The figure is named for the base.
Edges:
* The segment where the faces intersect.
Vertex:
* Where the segments intersect.
Regular Prism:
* A prism with the regular polygons as the
bases.
Pyramid:
* A polyhedron that has only one base.
Triangular Prism
Rectangular Prism
* All faces, except one (the base) intersect at
a single point, the vertex.
* Always named for the shape of the base.
Square Pyramid
Regular Polyhedron:
* A polyhedron in which all of its faces are
regular congruent polygons. (All edges are
also congruent.)
* There are exactly 5 types of regular
polyhedra.
Platonic
PlatonicSolids:
Solids:
**The
The55regular
regulartypes
typesof
ofpolyhedra.
polyhedra.
**Named
Namedafter
afterPlato
Platowho
whodescribed
describedthem
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in
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journals.
There are three-dimensional figures that are
not polyhedrons.
Cylinder:
* A solid with congruent circular bases in
a pair of parallel planes.
Cone:
* A solid with only one base that is
circular in shape. It will have a vertex.
Sphere:
* A set of points in space that are a given
distance from a given point.
The 5 types are (All faces are regular
polygons):
* Tetrahedron: 4 faces, equilateral triangles.
* Hexahedron (Cube): 6 faces, squares.
* Octahedron: 8 faces, equilateral triangles.
* Dodecahedron: 12 faces, pentagons.
* Icosahedron: 20 faces, equilateral
triangles.
Cross Section:
* When a plane crosses (intersects) a solid
figure.
* It will be the shape that you get.
*Depending on how you slice it will depend
on the shape you get.
** Slicing parallel to the base will give you
the same shape as the base.
** Cutting to intersect the bases will result
in a different shape.
** Cutting through the solid at an angle
will result in a shape of the base, just
altered a bit.
2. Identify each solid. Name the bases, faces,
edges, and vertices.
Example:
Cut an orange in half, you are looking at a
circle.
Cut a box down the center, you can be
looking at a rectangle.
Cut a soda can through the bases, down,
you will be looking at a rectangle.
a.
G
Bases:
B
Faces:
A
F
C
H
E
D
Edges:
Vertices:
b.
P
Bases:
Faces:
Q
Edges:
Vertices:
3. A customer ordered a two-layer cake.
Describe how the cake can be made into a
rectangle, a square or a triangle.
Rectangular Prism Cake:
parallel to bases:
through bases:
Circular Cake (cylinder):
parallel to bases:
diagonal
through bases:
Section 12-1 Three Dimensional Figures
pg. 639 - 642
#2, 3, 5, 7, 9, 11, 14-16, 20, 26 - 30, 45,
50, 54, 58, 60, 61