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2 Determine whether the two polygons are similar. If so, give the similarity ratio. 1) 2) )Not similar. 2)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

CONFIDENTIAL4 Three-Dimensional Figures TERM EXAMPLE A Prism is formed by two parallel congruent polygonal faces called bases connected by faces that are parallelograms. Bases A cylinder is formed by two parallel congruent circular bases and curved surface that connects the bases. Bases

CONFIDENTIAL5 TERM EXAMPLE A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex. Vertex Base A cone is formed by a circular base and a curved surface that connects the base to a vertex. Base Vertex

CONFIDENTIAL6 A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases. Triangular Prism Rectangular Prism Pentagonal Prism Hexagonal Prism Next Page:

CONFIDENTIAL 7 Triangular pyramid Rectangular pyramid Pentagonal pyramid Hexagonal pyramid

CONFIDENTIAL8 Classifying Three-Dimensional Figures Classify each figure. Name the vertices, edges, and bases. A. A B C D E Rectangular pyramid Vertices: A,B,C,D,E Edges: AB, BC, CD, AD, AE,BE, CE, DE Base: rectangle ABCD Next Page:

CONFIDENTIAL9 B. Q P Cylinder Vertices: none Edges: none Bases: P and Q Cylinder

CONFIDENTIAL10 Now you try! Classify each figure. Name the vertices, edges, and bases. N a) b) T U V X W Y a) Vertices: none Edges: none Bases: °P O b) Vertices: U, V, W, X, Y, Z Edges: TU, TV, YV, YX, WX, WT Base: triangle WXY

CONFIDENTIAL11 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.

CONFIDENTIAL12 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.

CONFIDENTIAL13 B) The net has one square face. The remaining faces are triangles, so the net forms a square pyramid.

CONFIDENTIAL14 Now you try! 2 a) Describe the three-dimensional figure that can be made from the given net. b) 2a) Triangular pyramid 2b) Cylinder

CONFIDENTIAL15 A cross section is the intersection of a three- dimensional figure and a plane.

CONFIDENTIAL16 Describing Cross Sections of Three- Dimensional Figures Describe each cross section. A The cross section is a triangle.

CONFIDENTIAL17 B The cross section is a circle.

CONFIDENTIAL18 Now you try! Describe each cross section. 3 a) b) 3a) Hexagon 3b) triangle

CONFIDENTIAL19 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 A square Cut parallel to the bases.

CONFIDENTIAL20 B a hexagon Cut through the midpoints of the edges.

CONFIDENTIAL21 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.

CONFIDENTIAL22 Now some problems for you to practice !

CONFIDENTIAL23 1)A ? has two circular bases. (prism, cylinder, or cone) Assessment 1) cylinder

CONFIDENTIAL24 2) Classify each figure. Name the vertices, edges, and bases. a) B A b) K G J D C E F H 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

CONFIDENTIAL25 3) Describe the three-dimensional figure that can be made from the given net. a) 3a) Rectangular Prism

CONFIDENTIAL 26 b) 3b) Cone

CONFIDENTIAL27 4) Describe each cross section. a) b) 4a) CIRCLE 4b) PENTAGON

CONFIDENTIAL28 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)A circle b) A rectangle 5a) Cut parallel to the bases 5b) Cut perpendicular to the bases

CONFIDENTIAL29 Let’s review 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

CONFIDENTIAL30 Three-Dimensional Figures TERM EXAMPLE A Prism is formed by two parallel congruent polygonal faces called bases connected by faces that are parallelograms. Bases A cylinder is formed by two parallel congruent circular bases and curved surface that connects the bases. Bases

CONFIDENTIAL31 TERM EXAMPLE A pyramid is formed by a polygonal base and triangular faces that meet at a common vertex. Vertex Base A cone is formed by a circular base and a curved surface that connects the base to a vertex. Base Vertex

CONFIDENTIAL32 A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases. Triangular Prism Rectangular Prism Pentagonal Prism Hexagonal Prism Next Page:

CONFIDENTIAL33 Triangular pyramid Rectangular pyramid Pentagonal pyramid Hexagonal pyramid

CONFIDENTIAL34 Classifying Three-Dimensional Figures Classify each figure. Name the vertices, edges, and bases. A. A B C D E Rectangular pyramid Vertices: A,B,C,D,E Edges: AB, BC, CD, AD, AE,BE, CE, DE Base: rectangle ABCD Next Page:

CONFIDENTIAL35 B. Q P Cylinder Vertices: none Edges: none Bases: P and Q Cylinder

CONFIDENTIAL36 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.

CONFIDENTIAL37 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.

CONFIDENTIAL38 B) The net has one square face. The remaining faces are triangles, so the net forms a square pyramid.

CONFIDENTIAL39 Describing Cross Sections of Three- Dimensional Figures Describe each cross section. A The cross section is a triangle.

CONFIDENTIAL40 B The cross section is a circle.

CONFIDENTIAL41 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 A square Cut parallel to the bases.

CONFIDENTIAL42 B a hexagon Cut through the midpoints of the edges.

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