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Understanding Three-Dimensional Figures: Prisms, Pyramids, and Spatial Relationships

This lesson covers the identification and drawing of three-dimensional figures such as prisms and pyramids. Students will learn key vocabulary including coplanar, skew lines, and properties of polyhedra. The lesson focuses on understanding relationships between planes and lines, identifying parallel planes, and drawing diagonals. Examples and exercises are included to illustrate how to classify solids, count edges, vertices, and faces, and analyze architectural drawings through top, front, and side views.

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Understanding Three-Dimensional Figures: Prisms, Pyramids, and Spatial Relationships

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Presentation Transcript

  1. Splash Screen

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

  3. 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

  4. A B C D Name a plane that is parallel to plane QUXT. A. plane QRST B. plane UVWX C. plane QRVU D. plane RVWS Example 1

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

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

  7. 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

  8. A B C D 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 Example 3

  9. 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

  10. A B C D 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 Example 4

  11. 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

  12. A B C D 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 Example 5

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

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

  15. End of the Lesson End of the Lesson

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