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Geometry Solid Geometry

Geometry Solid Geometry. Warm Up. Determine whether the two polygons are similar. If so, give the similarity ratio. 1). 2). 8. 42.5. 2. 2. 11.9. 8. 40.8. 12. 24. 4. 4. 7. 25. 12. Not similar. Similar. Similarity ratio = 1.7. Solid Geometry.

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Geometry Solid Geometry

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  1. GeometrySolid Geometry CONFIDENTIAL

  2. Warm Up Determine whether the two polygons are similar. If so, give the similarity ratio. 1) 2) 8 42.5 2 2 11.9 8 40.8 12 24 4 4 7 25 12 • Not similar. • Similar. Similarity ratio = 1.7 CONFIDENTIAL

  3. Solid Geometry 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. Face Edge Vertex CONFIDENTIAL

  4. Three-Dimensional Figures TERM EXAMPLE APrismis formed by two parallel congruent polygonal faces called bases connected by faces that are parallelograms. Bases Acylinderis formed by two parallel congruent circular bases and curved surface that connects the bases. Bases CONFIDENTIAL

  5. Vertex TERM EXAMPLE A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex. Base Vertex A cone is formed by a circular base and a curved surface that connects the base to a vertex. Base CONFIDENTIAL

  6. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases. Rectangular Prism Pentagonal Prism Triangular Prism Hexagonal Prism Next Page: CONFIDENTIAL

  7. Pentagonal pyramid Rectangular pyramid Triangular pyramid Hexagonal pyramid CONFIDENTIAL

  8. Classifying Three-Dimensional Figures Classify each figure. Name the vertices, edges, and bases. A. E Rectangular pyramid Vertices: A,B,C,D,E Edges: AB, BC, CD, AD, AE,BE, CE, DE Base: rectangle ABCD A D B C Rectangular pyramid Next Page: CONFIDENTIAL

  9. B. P Cylinder Vertices: none Edges: none Bases: P and Q Q Cylinder CONFIDENTIAL

  10. Now you try! Classify each figure. Name the vertices, edges, and bases. b) a) V T N U O Y W a) Vertices: none Edges: none Bases: °P b) Vertices: U, V, W, X, Y, Z Edges: TU, TV, YV, YX, WX, WT Base: triangle WXY X CONFIDENTIAL

  11. A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face. CONFIDENTIAL

  12. Identifying a Three-Dimensional Figure From a Net Describe the three-dimensional figure that can be made from the given net. A) The net has two congruent triangular faces. The remaining faces are parallelograms, so the net forms a triangular prism. CONFIDENTIAL

  13. B) The net has one square face. The remaining faces are triangles, so the net forms a square pyramid. CONFIDENTIAL

  14. Now you try! Describe the three-dimensional figure that can be made from the given net. 2 a) b) 2a) Triangular pyramid 2b) Cylinder CONFIDENTIAL

  15. Across section is the intersection of a three-dimensional figure and a plane. CONFIDENTIAL

  16. Describing Cross Sections of Three-Dimensional Figures Describe each cross section. The cross section is a triangle. A CONFIDENTIAL

  17. The cross section is a circle. B CONFIDENTIAL

  18. Now you try! Describe each cross section. b) 3 a) 3a) Hexagon 3b) triangle CONFIDENTIAL

  19. Food Application A chef is slicing a cube-shaped watermelon for a buffet. How can the chef cut the watermelon to make a slice of each shape? A square A Cut parallel to the bases. CONFIDENTIAL

  20. B a hexagon Cut through the midpoints of the edges. CONFIDENTIAL

  21. Now you try! 4) How can a chef cut a cube-shaped watermelon to make slices with triangular faces? 4) Cut through midpoints of the bases. CONFIDENTIAL

  22. Now some problems for you to practice ! CONFIDENTIAL

  23. Assessment • A ? has two circular bases. • (prism, cylinder, or cone) 1) cylinder CONFIDENTIAL

  24. 2) Classify each figure. Name the vertices, edges, and bases. 2a) Vertices: none Edges: none Bases: °B 2b) ) Vertices: C, D, E, F, G, H, J, K Edges: CD, CF, CK, DJ, EH, ED, EF, JH, GK, GH, FG, EF Base: Rectangle CDEF A b) a) G H J K E F B C D CONFIDENTIAL

  25. 3) Describe the three-dimensional figure that can be made from the given net. 3a) Rectangular Prism a) CONFIDENTIAL

  26. b) 3b) Cone CONFIDENTIAL

  27. 4) Describe each cross section. b) a) 4a) CIRCLE 4b) PENTAGON CONFIDENTIAL

  28. 5) A sculptor has a cylindrical piece of clay. How can the sculptor slice the clay to make a slice of each given shape? • A circle • b) A rectangle 5a) Cut parallel to the bases 5b) Cut perpendicular to the bases CONFIDENTIAL

  29. Let’s review Solid Geometry Face Edge 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. Vertex CONFIDENTIAL

  30. Three-Dimensional Figures TERM EXAMPLE APrismis formed by two parallel congruent polygonal faces called bases connected by faces that are parallelograms. Bases Acylinderis formed by two parallel congruent circular bases and curved surface that connects the bases. Bases CONFIDENTIAL

  31. Vertex TERM EXAMPLE A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex. Base Vertex A cone is formed by a circular base and a curved surface that connects the base to a vertex. Base CONFIDENTIAL

  32. A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases. Rectangular Prism Pentagonal Prism Triangular Prism Hexagonal Prism Next Page: CONFIDENTIAL

  33. Pentagonal pyramid Rectangular pyramid Triangular pyramid Hexagonal pyramid CONFIDENTIAL

  34. Classifying Three-Dimensional Figures Classify each figure. Name the vertices, edges, and bases. A. E Rectangular pyramid Vertices: A,B,C,D,E Edges: AB, BC, CD, AD, AE,BE, CE, DE Base: rectangle ABCD A D B C Rectangular pyramid Next Page: CONFIDENTIAL

  35. B. P Cylinder Vertices: none Edges: none Bases: P and Q Q Cylinder CONFIDENTIAL

  36. A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face. CONFIDENTIAL

  37. Identifying a Three-Dimensional Figure From a Net Describe the three-dimensional figure that can be made from the given net. A) The net has two congruent triangular faces. The remaining faces are parallelograms, so the net forms a triangular prism. CONFIDENTIAL

  38. B) The net has one square face. The remaining faces are triangles, so the net forms a square pyramid. CONFIDENTIAL

  39. Describing Cross Sections of Three-Dimensional Figures Describe each cross section. The cross section is a triangle. A CONFIDENTIAL

  40. The cross section is a circle. B CONFIDENTIAL

  41. Food Application A chef is slicing a cube-shaped watermelon for a buffet. How can the chef cut the watermelon to make a slice of each shape? A square A Cut parallel to the bases. CONFIDENTIAL

  42. B a hexagon Cut through the midpoints of the edges. CONFIDENTIAL

  43. You did a great job today! CONFIDENTIAL

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