Download - Geometry Solid Geometry
CONFIDENTIAL 1
CONFIDENTIAL 2
Determine whether the two polygons are similar. If so, give the similarity ratio.
1) 2)
8
8
2 2
12
4
12
4
11.942.5
40.8
7
24
25
CONFIDENTIAL3
Solid GeometrySolid Geometry
Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the
intersection of two faces. A vertex is the point that is the intersection of three or more faces.
Face Edge
Vertex
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Three-Dimensional Figures Three-Dimensional Figures
TERM EXAMPLE
A Prism is formed by two parallel congruent polygonal faces called bases
connected by faces that are parallelograms.
Bases
A cylinder is formed by two parallel congruent circular bases and curved
surface that connects the bases. Bases
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TERM EXAMPLE
A pyramid is formed by a polygonal base and triangular faces that meet at
a common vertex.
Vertex
Base
A cone is formed by a circular base and a curved surface that connects
the base to a vertex.Base
Vertex
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A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
TriangularPrism
RectangularPrism
PentagonalPrism
HexagonalPrism Next Page:
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Triangularpyramid
Rectangularpyramid
Pentagonalpyramid
Hexagonalpyramid
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Classifying Three-Dimensional Figures
Classify each figure. Name the vertices, edges, and bases.
A.
A
B C
D
E
Rectangular pyramid
Rectangular pyramid
Vertices: A,B,C,D,E
Edges: AB, BC, CD, AD, AE,BE, CE, DE
Base: rectangle ABCD
Next Page:
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B.
Q
P
CylinderVertices: noneEdges: none
Bases: P and Q
Cylinder
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Now you try!
Classify each figure. Name the vertices, edges, and bases.
N
a) b)
T
U
V
X
W YO
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A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form
the three-dimensional figure. To identify a three-dimensional figure from a net, look at the
number of faces and the shape of each face.
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Identifying a Three-Dimensional Figure From a Net
Describe the three-dimensional figure that can be made from the given net.
A)
The net has two congruent triangular faces. The remaining faces are parallelograms, so the net forms a triangular prism.
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B)
The net has one square face. The remaining faces are triangles, so the net forms a square pyramid.
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Now you try!
2 a)
Describe the three-dimensional figure that can be made from the given net.
b)
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A cross section is the intersection of a three-dimensional figure and a plane.
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Describing Cross Sections of Three-Dimensional Figures
Describe each cross section.
A The cross section is a triangle.
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B The cross section is a circle.
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Now you try!
Describe each cross section.
3 a) b)
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Food Application
A chef is slicing a cube-shaped watermelon for a buffet. How can the chef cut the watermelon to
make a slice of each shape?
A A square
Cut parallel to the bases.
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B a hexagon
Cut through the midpoints of the edges.
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Now you try!
4) How can a chef cut a cube-shaped watermelon to make slices with triangular faces?
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Now some problems for you to practice !
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1) A ? has two circular bases.
(prism, cylinder, or cone)
Assessment
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2) Classify each figure. Name the vertices, edges, and bases.
a)
B
Ab)
K
G
J
DC
EF
H
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3) Describe the three-dimensional figure that can be made from the given net.
a)
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b)
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4) Describe each cross section.
a) b)
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5) A sculptor has a cylindrical piece of clay. How can the sculptor slice the clay to make a slice of each given shape?
a) A circle
b) A rectangle
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Let’s review
Solid GeometrySolid Geometry
Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the
intersection of two faces. A vertex is the point that is the intersection of three or more faces.
Face Edge
Vertex
CONFIDENTIAL 30
Three-Dimensional Figures Three-Dimensional Figures
TERM EXAMPLE
A Prism is formed by two parallel congruent polygonal faces called bases
connected by faces that are parallelograms.
Bases
A cylinder is formed by two parallel congruent circular bases and curved
surface that connects the bases. Bases
CONFIDENTIAL 31
TERM EXAMPLE
A pyramid is formed by a polygonal base and triangular faces that meet at
a common vertex.
Vertex
Base
A cone is formed by a circular base and a curved surface that connects
the base to a vertex.Base
Vertex
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A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.
TriangularPrism
RectangularPrism
PentagonalPrism
HexagonalPrism Next Page:
CONFIDENTIAL 33
Triangularpyramid
Rectangularpyramid
Pentagonalpyramid
Hexagonalpyramid
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Classifying Three-Dimensional Figures
Classify each figure. Name the vertices, edges, and bases.
A.
A
B C
D
E
Rectangular pyramid
Rectangular pyramid
Vertices: A,B,C,D,E
Edges: AB, BC, CD, AD, AE,BE, CE, DE
Base: rectangle ABCD
Next Page:
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B.
Q
P
CylinderVertices: noneEdges: none
Bases: P and Q
Cylinder
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A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form
the three-dimensional figure. To identify a three-dimensional figure from a net, look at the
number of faces and the shape of each face.
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Identifying a Three-Dimensional Figure From a Net
Describe the three-dimensional figure that can be made from the given net.
A)
The net has two congruent triangular faces. The remaining faces are parallelograms, so the net forms a triangular prism.
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B)
The net has one square face. The remaining faces are triangles, so the net forms a square pyramid.
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Describing Cross Sections of Three-Dimensional Figures
Describe each cross section.
A The cross section is a triangle.
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B The cross section is a circle.
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Food Application
A chef is slicing a cube-shaped watermelon for a buffet. How can the chef cut the watermelon to
make a slice of each shape?
A A square
Cut parallel to the bases.
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B a hexagon
Cut through the midpoints of the edges.
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