course 2 10-1 introduction to three-dimensional figures 10-1 introduction to three-dimensional...
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Course 2
10-1 Introduction to Three-Dimensional Figures10-1 Introduction to Three-Dimensional Figures
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Course 2
10-1 Introduction to Three-Dimensional Figures
Warm UpIdentify 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
Course 2
10-1 Introduction to Three-Dimensional Figures
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
Course 2
10-1 Introduction to Three-Dimensional Figures
Learn to identify various three-dimensional figures.
Course 2
10-1 Introduction to Three-Dimensional Figures
Vocabulary
faceedgepolyhedronvertexbase
prism
pyramidcylindercone
Course 2
10-1 Introduction to Three-Dimensional Figures
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.
Course 2
10-1 Introduction to Three-Dimensional Figures
Prisms
A prism is a polyhedron that has two parallel, congruent bases. The bases can be any polygon. The other faces are parallelograms.
Course 2
10-1 Introduction to Three-Dimensional Figures
Pyramids
A pyramid is a polyhedron that has one base. The base can be any polygon. The other faces are triangles.
Course 2
10-1 Introduction to Three-Dimensional Figures
Identify the bases and faces of the figure. Then name the figure.
Additional Example 1A: Naming Prisms and Pyramids
There are two octagonal bases.
The figure is an octagonal prism.
There are eight rectangular faces.
Course 2
10-1 Introduction to Three-Dimensional Figures
Additional Example 1B: Naming Prisms and Pyramids
There is one base, and it is a pentagon.
There are five triangular faces.
The figure is a pentagonal pyramid.
Identify the bases and faces of the figure. Then name the figure.
Course 2
10-1 Introduction to Three-Dimensional Figures
Additional Example 1C: Naming Prisms and Pyramids
There is one base, and it is a triangle.
There are three triangular faces.
The figure is a triangular pyramid.
Identify the bases and faces of the figure. Then name the figure.
Course 2
10-1 Introduction to Three-Dimensional Figures
Additional Example 1D: Naming Prisms and Pyramids
There are two bases, and they are both hexagons.
There are six rectangular faces.
The figure is a hexagonal prism.
Identify the bases and faces of the figure. Then name the figure.
Course 2
10-1 Introduction to Three-Dimensional Figures
Check It Out: Example 1A
There are two bases and they are both triangles.
There are three rectangular faces.
The figure is a triangular prism.
Identify the bases and faces of the figure. Then name the figure.
Course 2
10-1 Introduction to Three-Dimensional Figures
Check It Out: Example 1B
All faces and bases are congruent squares.
The figure is a cube.
Identify the bases and faces of the figure. Then name the figure.
Course 2
10-1 Introduction to Three-Dimensional Figures
Other three-dimensional figures include cylinders and cones. These figures are not polyhedrons because they are not made of faces that are all polygons.
Course 2
10-1 Introduction to Three-Dimensional Figures
You can use properties to classify three-dimensional figures.
Course 2
10-1 Introduction to Three-Dimensional Figures
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
Additional Example 2A: Classifying Three-Dimensional Figures
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.
Course 2
10-1 Introduction to Three-Dimensional Figures
There is one circular base.
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
Additional Example 2B: Classifying Three-Dimensional Figures
The faces are not all polygons, so the figure is not a polyhedron.
The figure is a cone.
Course 2
10-1 Introduction to Three-Dimensional Figures
There are two circular base.
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
Additional Example 2C: Classifying Three-Dimensional Figures
The faces are not all polygons, so the figure is not a polyhedron.
The figure is a cylinder.
Course 2
10-1 Introduction to Three-Dimensional Figures
Check It Out: Example 2A
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
There is one circular base for the top figure and two circular bases for the bottom figure.
The faces are not all polygons, so the figure is not a polyhedron.
The figure is made up of a cylinder and a cone.
Course 2
10-1 Introduction to Three-Dimensional Figures
Check It Out: Example 2B
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
There are two triangular bases for the figure.
The faces are all polygons, so the figure is a polyhedron.
The figure is a triangular prism.
Course 2
10-1 Introduction to Three-Dimensional Figures
Check It Out: Example 2C
Classify each figure as a polyhedron or not a polyhedron. Then name the figure.
There is one rectangular base for the figure.
The faces are all polygons, so the figure is a polyhedron.
The figure is a rectangular pyramid.
Course 2
10-1 Introduction to Three-Dimensional Figures
Lesson Quiz: Part IIdentify the bases and faces of each figure. Then name each figure.
Two pentagon bases, 5 rectangular faces; pentagonal prism
One square base, 4 triangular faces; square pyramid
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