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**10-1 Introduction to Three-Dimensional Figures Warm Up**

Course 2 Warm Up Problem of the Day Lesson Presentation

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**Warm Up Identify each two-dimensional figure described.**

1. four sides that are all congruent 2. six sides 3. four sides with parallel opposite sides 4. four right angles and four congruent sides rhombus hexagon parallelogram square

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Problem of the Day If the figure shown is folded into a cube so that 6 is on the top, what number would be on the bottom? 2

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**Learn to identify various three-dimensional figures.**

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**Vocabulary prism face pyramid edge cylinder polyhedron vertex cone**

base

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**Three-dimensional figures, or solids, have length, width, and height**

Three-dimensional figures, or solids, have length, width, and height. A flat surface of a solid is a face. An edge is where two faces meet. A polyhedron is a three-dimensional figure whose faces are all polygons. A vertex of a polyhedron is a point where three or more edges meet. The face that is used to name a polyhedron is called a base. A prism has two bases, and a pyramid has one.

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Prisms A prism is a polyhedron that has two parallel, congruent bases. The bases can be any polygon. The other faces are parallelograms.

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Pyramids A pyramid is a polyhedron that has one base. The base can be any polygon. The other faces are triangles.

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**Additional Example 1A: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. There are two octagonal bases. There are eight rectangular faces. The figure is an octagonal prism.

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**Additional Example 1B: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. There is one base, and it is a pentagon. There are five triangular faces. The figure is a pentagonal pyramid.

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**Additional Example 1C: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. There is one base, and it is a triangle. There are three triangular faces. The figure is a triangular pyramid.

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**Additional Example 1D: Naming Prisms and Pyramids**

Identify the bases and faces of the figure. Then name the figure. There are two bases, and they are both hexagons. There are six rectangular faces. The figure is a hexagonal prism.

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Check It Out: Example 1A Identify the bases and faces of the figure. Then name the figure. There are two bases and they are both triangles. There are three rectangular faces. The figure is a triangular prism.

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Check It Out: Example 1B Identify the bases and faces of the figure. Then name the figure. All faces and bases are congruent squares. The figure is a cube.

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**Other three-dimensional figures include cylinders and cones**

Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because they are not made of faces that are all polygons.

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**You can use properties to classify three-dimensional figures.**

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**Additional Example 2A: Classifying Three-Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are all polygons, so the figure is a polyhedron. There is one rectangular base for each figure. The figure is made up of a rectangular pyramid and a rectangular prism.

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**Additional Example 2B: Classifying Three-Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base. The figure is a cone.

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**Additional Example 2C: Classifying Three-Dimensional Figures**

Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are not all polygons, so the figure is not a polyhedron. There are two circular base. The figure is a cylinder.

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Check It Out: Example 2A Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are not all polygons, so the figure is not a polyhedron. There is one circular base for the top figure and two circular bases for the bottom figure. The figure is made up of a cylinder and a cone.

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Check It Out: Example 2B Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are all polygons, so the figure is a polyhedron. There are two triangular bases for the figure. The figure is a triangular prism.

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Check It Out: Example 2C Classify each figure as a polyhedron or not a polyhedron. Then name the figure. The faces are all polygons, so the figure is a polyhedron. There is one rectangular base for the figure. The figure is a rectangular pyramid.

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Lesson Quiz: Part I Identify the bases and faces of each figure. Then name each figure. 1. One square base, 4 triangular faces; square pyramid 2. Two pentagon bases, 5 rectangular faces; pentagonal prism

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Lesson Quiz: Part II Classify each figure as a polyhedron or not a polyhedron. Then name the figure. 3. polyhedron, rectangular prism polyhedron, triangular prism 4.

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