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**Identify and draw three-dimensional figures.**

coplanar vertex diagonal skew lines prism base pyramid parallel solid polyhedron edge face Main Idea/Vocabulary

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**Identify Relationships**

Name a plane that is parallel to plane GKJ. In order for a plane to be parallel to plane GKJ , it cannot intersect it. Answer: Therefore, plane LPN is parallel to plane GKJ. Example 1

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**Name a plane that is parallel to plane QUXT.**

A. plane QRST B. plane UVWX C. plane QRVU D. plane RVWS A B C D Example 1

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**Identify Relationships**

Identify a segment that is skew to JN. Skew lines cannot intersect and cannot be coplanar. Answer: Therefore, segment LM is skew to segment JN. Example 2

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A. B. C. D. A B C D Example 2

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**Identify Relationships**

Identify two sets of points between which a diagonal can be drawn. A diagonal connects two opposite points on parallel planes. Answer: Lines drawn between points G and N and points L and J would form diagonals. Example 3

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**Identify a set of points between which a diagonal can be drawn.**

A. points S and Q B. points V and X C. points Q and W D. points R and W A B C D Example 3

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**Identify Prisms and Pyramids**

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has two parallel congruent bases that are octagons, so it is an octagonal prism. The other eight faces are rectangles. It has a total of 10 faces, 24 edges, and 16 vertices. Example 4

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**Identify the solid. Name the number and shapes of the faces**

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. A. triangular prism; 2 triangular faces, 3 rectangular faces, 9 edges, and 6 vertices B. pentagonal pyramid; 3 triangular faces, 2 rectangular faces, 9 edges, and 6 vertices C. rectangular prism; 2 triangular faces, 3 rectangular faces, 9 edges, and 6 vertices D. cylinder; 2 triangular faces, 3 rectangular faces, 9 edges, and 6 vertices A B C D Example 4

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**Identify Prisms and Pyramids**

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. Answer: The figure has one base that is a rectangle, so it is a rectangular pyramid. The other four faces are triangles. It has a total of 5 faces, 8 edges, and 5 vertices. Example 5

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**Identify the solid. Name the number and shapes of the faces**

Identify the solid. Name the number and shapes of the faces. Then name the number of edges and vertices. A. triangular prism; 1 pentagonal base, 3 triangular faces, 10 edges, and 6 vertices B. pentagonal pyramid; 1 pentagonal base, 5 triangular faces, 10 edges, and 6 vertices C. rectangular prism; 1 pentagonal base, 5 triangular faces, 9 edges, and 6 vertices D. octagonal prism; 8 triangular faces, 1 pentagonal face, 9 edges, and 6 vertices A B C D Example 5

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Analyze Drawings ARCHITECTURE The plans for a hotel fireplace are shown below. Draw and label the top, front, and side views. Answer: Example 6

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**ARCHITECTURE The plans for a building are shown below**

ARCHITECTURE The plans for a building are shown below. Draw and label the top, front, and side views. A. B. C. D. A B C D Example 6

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(over Lesson 7-3) Find the area of the figure shown. Round to the nearest tenth if necessary. A. 18 cm2 B. 27 cm2 C. 36 cm2 D. 45 cm2 A B C D Five Minute Check 1

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(over Lesson 7-3) Find the area of the figure shown. Round to the nearest tenth if necessary. A. 25 mi2 B. 36 mi2 C. 67 mi2 D. 74 mi2 A B C D Five Minute Check 2

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(over Lesson 7-3) What is the area of the figure shown at the right? Round to the nearest tenth if necessary. A in2 B in2 C in2 D in2 A B C D Five Minute Check 3

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Find the volumes of prisms and cylinders.

Find the volumes of prisms and cylinders.

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