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Geometry Solid Geometry. Warm Up. Determine whether the two polygons are similar. If so, give the similarity ratio. 1). 2). 8. 42.5. 2. 2. 11.9. 8. 40.8. 12. 24. 4. 4. 7. 25. 12. Solid Geometry. - PowerPoint PPT Presentation
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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
CONFIDENTIAL 4
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 5
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:
CONFIDENTIAL7
Triangularpyramid
Rectangularpyramid
Pentagonalpyramid
Hexagonalpyramid
CONFIDENTIAL 8
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:
CONFIDENTIAL 9
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.
CONFIDENTIAL 12
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.
CONFIDENTIAL 13
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)
CONFIDENTIAL 19
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
CONFIDENTIAL 32
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
CONFIDENTIAL 34
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:
CONFIDENTIAL 35
B.
Q
P
CylinderVertices: noneEdges: none
Bases: P and Q
Cylinder
CONFIDENTIAL 36
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.
CONFIDENTIAL 37
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.
CONFIDENTIAL 39
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.
CONFIDENTIAL 43
