8-7Introduction to Three-Dimensional Figures
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
8-7Introduction 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
8-7Introduction 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
8-7Introduction to Three-Dimensional Figures
Prep for MA.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones.Review of MA.5.G.3.1
Sunshine State Standards
8-7Introduction to Three-Dimensional Figures
Vocabulary
faceedgepolyhedronvertexbase
prism
pyramidcylinderconesphere
8-7Introduction to Three-Dimensional Figures
Three-dimensional figures have three dimensions: length, width, and height. A flat surface of a three-dimensional figure 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 a base.
A prism has two bases, and a pyramid has one.
8-7Introduction to Three-Dimensional Figures
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction to Three-Dimensional Figures
Other three-dimensional figures include cylinders, cones, and spheres. These figures are not polyhedrons because they are not made of faces that are all polygons.
8-7Introduction to Three-Dimensional Figures
You can use properties to classify three-dimensional figures.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction to Three-Dimensional Figures
There are two circular bases.
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.
8-7Introduction 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.
8-7Introduction 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.
8-7Introduction 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 square base for the figure.
The faces are all polygons, so the figure is a polyhedron.
The figure is a square pyramid.
8-7Introduction to Three-Dimensional Figures
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
8-7Introduction 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
1.
2.
8-7Introduction to Three-Dimensional Figures
Lesson Quiz: Part IIClassify each figure as a polyhedron or not a polyhedron. Then name the figure.
polyhedron, rectangular prism
polyhedron, triangular prism
3.
4.
8-7Introduction to Three-Dimensional Figures
1. Identify the bases and faces, and then the name of the given figure.
A. pentagon; triangles; pentagonal prism
B. hexagon; triangles; hexagonal prism
C. pentagon; triangles; pentagonal pyramid
D. hexagon; triangles; hexagonal pyramid
Lesson Quiz for Student Response Systems
8-7Introduction to Three-Dimensional Figures
2. Identify the bases and faces, and then the name of the given figure.
A. pentagon; triangles; pentagonal pyramid
B. heptagon; triangles; heptagonal pyramid
C. pentagon; rectangles; pentagonal prism
D. heptagon; rectangles; heptagonal prism
Lesson Quiz for Student Response Systems
8-7Introduction to Three-Dimensional Figures
3. Classify the figure as a polyhedron or not a polyhedron, and then name the given figure.
A. polyhedron; pentagonal prism
B. polyhedron; pentagonal pyramid
C. not a polyhedron; cylinder
D. not a polyhedron; cone
Lesson Quiz for Student Response Systems
8-7Introduction to Three-Dimensional Figures
4. Classify the figure as a polyhedron or not a polyhedron, and then name the given figure.
A. polyhedron; heptagonal prism
B. polyhedron; nonagonal pyramid
C. not a polyhedron; cylinder
D. not a polyhedron; cone
Lesson Quiz for Student Response Systems