3.4 Polyhedrons and Prisms

Objective: to name polyhedrons and prisms

Warm UpClassify each polygon.

1. a polygon with three congruent sides

2. a polygon with six congruent sides and six congruent angles

3. a polygon with four sides and with opposite sides parallel and congruent

equilateral triangle

regular hexagon

parallelogram

Polyhedron – a three-dimensional figure in which each surface is shaped like a polygon

Face – a flat surface that is shaped like a polygonEdge – the segment formed by the intersection of two facesVertex – a point at which three or more edges intersectPrism – a polyhedron with two faces that have the same size and

shape and lie in parallel planesBase – the two faces on a prism that are parallel to each otherCylinder – is not a prism because it has two circles as basesPyramid – is not a prism because it does not have two basesLateral face – the faces that are not the bases, they are shaped like

a parallelogram.Right – all lateral faces are rectangles that lie in planes perpendicular to the bases.Oblique – figures that are not right, they are slanted like they are

getting pushed over.

Vocabulary

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.

A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

Example 1A: Classifying Three-Dimensional Figures

Classify the figure. Name the vertices, edges, and bases.

cube

vertices: A, B, C, D, E, F, G, H

bases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF

edges:

Is this a prism?

Example 1B: Classifying Three-Dimensional Figures

Classify the figure. Name the vertices, edges, and bases.

pentagonal pyramid

vertices: A, B, C, D, E, F

base: ABCDE

edges:

Is this a prism?

Check It Out! Example 1a

Classify the figure. Name the vertices, edges, and bases.

vertex: N

cone

edges: none

base: •M

M

Is this a prism?

Check It Out! Example 1b

Classify the figure. Name the vertices, edges, and bases.

triangular prism

bases: ∆TUV, ∆WXY

vertices: T, U, V, W, X, Y

edges:

Is this a prism?

Check It Out! Example 3a

Is this a prism? If it is name it.

Hexagonal prism

Example 4A: Food Application

Is this piece of cheese a prism? If it is, name it.

Triangular Prism

Check It Out! Example 4

Is this watermelon a prism? If so, name it.

Cube or rectangular prism

Lesson Quiz:

1. Classify the figure. Name the vertices, edges, and bases.

triangular prism; vertices: A, B, C, D, E, F;

bases: ∆ABC and ∆DEF

edges:

Homework

section 3-4 # 1-19