Transcript Slide 1

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Determine whether the two polygons are similar. If
so, give the similarity ratio.
1)
2)
8
2
2
42.5
11.9
8
40.8
12
24
4
4
12
7
25
1) Not similar.
2) Similar. Similarity ratio = 1.7
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Solid Geometry
Face
Edge
Vertex
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.
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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
Vertex
A pyramid is formed by a polygonal
base and triangular faces that meet at
a common vertex.
Base
Vertex
A cone is formed by a circular base
and a curved surface that connects
the base to a vertex.
Base
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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.
Triangular
Prism
Rectangular
Prism
Pentagonal
Prism
Hexagonal
Prism
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Triangular
pyramid
Pentagonal
pyramid
Rectangular
pyramid
Hexagonal
pyramid
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Classifying Three-Dimensional
Figures
Classify each figure. Name the vertices, edges, and bases.
E
A.
Rectangular pyramid
Vertices: A,B,C,D,E
Edges: AB, BC, CD, AD,
AE,BE, CE, DE
Base: rectangle ABCD
A
D
B
C
Rectangular pyramid
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B.
P
Cylinder
Vertices: none
Edges: none
Bases: P and Q
Q
Cylinder
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Now you try!
Classify each figure. Name the vertices, edges, and bases.
b)
a)
V
T
N
U
O
Y
W
a) Vertices: none b) Vertices: U, V, W, X, Y, Z
Edges: none Edges: TU, TV, YV, YX, WX, WT
Bases: °P
Base: triangle WXY
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A net is a diagram of the surfaces of a threedimensional 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!
Describe the three-dimensional figure that can be
made from the given net.
2 a)
b)
2a) Triangular pyramid
2b) Cylinder
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A cross section is the intersection of a threedimensional figure and a plane.
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Describing Cross Sections of ThreeDimensional 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)
3a) Hexagon
3b) triangle
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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?
4) Cut through midpoints of the bases.
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Now some problems for you to practice !
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Assessment
1) A
?
has two circular bases.
(prism, cylinder, or cone)
1) cylinder
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2) Classify each figure. Name the vertices, edges, and bases.
a)
A
2a) Vertices: none
Edges: none
b)
Bases: °B
G
2b) ) Vertices: C, D, E,
F, G, H, J, K
Edges: CD, CF, CK, DJ,
EH, ED, EF, JH,KGK, GH,
FG, EF
Base: Rectangle CDEF
H
J
E
F
B
C
D
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3) Describe the three-dimensional figure that can
be made from the given net.
a)
3a) Rectangular Prism
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b)
3b) Cone
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4) Describe each cross section.
b)
a)
4a) CIRCLE
4b) PENTAGON
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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
5a) Cut parallel to the bases
5b) Cut perpendicular to the bases
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Let’s review
Solid Geometry
Face
Edge
Vertex
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.
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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
Vertex
A pyramid is formed by a polygonal
base and triangular faces that meet at
a common vertex.
Base
Vertex
A cone is formed by a circular base
and a curved surface that connects
the base to a vertex.
Base
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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.
Triangular
Prism
Rectangular
Prism
Pentagonal
Prism
Hexagonal
Prism
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Triangular
pyramid
Pentagonal
pyramid
Rectangular
pyramid
Hexagonal
pyramid
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Classifying Three-Dimensional
Figures
Classify each figure. Name the vertices, edges, and bases.
E
A.
Rectangular pyramid
Vertices: A,B,C,D,E
Edges: AB, BC, CD, AD,
AE,BE, CE, DE
Base: rectangle ABCD
A
D
B
C
Rectangular pyramid
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B.
P
Cylinder
Vertices: none
Edges: none
Bases: P and Q
Q
Cylinder
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A net is a diagram of the surfaces of a threedimensional 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 ThreeDimensional 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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