Identify and draw three-dimensional figures. coplanar vertex diagonal skew lines prism base pyramid parallel solid polyhedron edge face Main Idea/Vocabulary

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

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

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

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

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

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

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

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

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

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

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

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

(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

(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

(over Lesson 7-3) What is the area of the figure shown at the right? Round to the nearest tenth if necessary. A. 80.5 in2 B. 85.7 in2 C. 161.0 in2 D. 105.0 in2 A B C D Five Minute Check 3

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