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Exam 17: Polyhedra

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Question 1

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What is the name of the shape below?

A) polyhedron
B) eight-gon
C) hexagonal prism
D) octahedron
E) L-pyramid

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Question 2

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Sketch a pentagonal pyramid. Be sure to include the hidden edges. Is your pyramid right or oblique?

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Question 3

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Which shapes are congruent? If none are congruent, explain how you know.

Give the BEST name for the three-dimensional shapes represented by the following pictures. Note: Angles that look like right angles are right angles in the three-dimensional shape. a. b. c. (a net) d. g. h.

I am a polyhedron with a total of nine faces. My eight lateral faces are isosceles triangles, all alike. My BEST name is:

How many faces CANNOT be seen in the drawing of a hexagonal pyramid?

Is it possible for the number of edges, the number of faces, and the number of vertices of a polyhedron to all be even? If so, give an example. If not, explain why not.

Complete the following sentences. A) An octagonal prism has _____ edges (in all) and _____ vertices. B) An n-gonal pyramid has _____ lateral edges and _____ faces. C) A prism that has 12 faces in all has _____ vertices. D) A polyhedron with 250 edges and 102 vertices has _____ faces.

Complete the following sentences. A) A prism with 16 vertices is a(n) _____ prism. B) A hexagonal prism has _____ edges, _____ vertices, and _____ faces. C) A pyramid with 60 edges has _____ vertices and _____ faces. D) A pentagonal prism has _____ edges, _____ vertices, and _____ faces.

What is a regular polyhedron?

Explain why a cube is a regular polyhedron.

State Euler's formula for polyhedra.

I am a polyhedron with a total of nine faces. My lateral faces are isosceles triangles. What is my full name?

A) There are _____ types of regular polyhedra. B) Name the types.

Which statement is safe to say about every square pyramid? I. Every lateral edge has the same length. II. all of the angles on each face are equal. III. Every base edge has the same length.

How many nets form a square pyramid? Sketch.

Which statement is TRUE for every square prism? I. Every angle in every face is a right triangle. II. Every lateral edge has the same length. III. All the edges have the same length.

One of the types of regular polyhedra was only discovered in 1914.

Give the BEST name for the represented shapes. A) B)

(Note to instructor: Preparation before the test is necessary.) For Model X on your table: 1) Draw a net. (You are not allowed to take the model on your table apart, but feel free to pick it up.) 2) Draw a picture of the model. 3) State the correct mathematical name for Model X, For Model Y on your table, draw a net.