Geometry Solid Geometry

GeometrySolid Geometry CONFIDENTIAL

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

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

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

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

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

Pentagonal pyramid Rectangular pyramid Triangular pyramid Hexagonal pyramid CONFIDENTIAL

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

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

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

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

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

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

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

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

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

The cross section is a circle. B CONFIDENTIAL

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

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

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

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

Now some problems for you to practice ! CONFIDENTIAL

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

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

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

b) 3b) Cone CONFIDENTIAL

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

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

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