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

1) Not similar.2) Similar. Similarity ratio = 1.7

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:

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 Y

a) Vertices: none Edges: none Bases: °P

O

b) Vertices: U, V, W, X, Y, ZEdges: TU, TV, YV, YX, WX, WTBase: triangle WXY

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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)

2a) Triangular pyramid2b) Cylinder

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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)

3a) Hexagon3b) triangle

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?

4) Cut through midpoints of the bases.

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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

1) cylinder

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2) Classify each figure. Name the vertices, edges, and bases.

a)

B

Ab)

K

G

J

DC

EF

H

2a) Vertices: none Edges: none Bases: °B

2b) ) Vertices: C, D, E, F, G, H, J, KEdges: CD, CF, CK, DJ, EH, ED, EF, JH, GK, GH, FG, EFBase: Rectangle CDEF

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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.

a) b)

4a) CIRCLE4b) 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 bases5b) Cut perpendicular to the bases

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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:

CONFIDENTIAL 35

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.

CONFIDENTIAL 43