# 12-1 Exploring Solids Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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• 12-1Exploring SolidsHolt GeometryWarm UpLesson PresentationLesson Quiz

• Warm UpClassify each polygon.

1. a polygon with three congruent sides

2. a polygon with six congruent sides and six congruent angles

3. a polygon with four sides and with opposite sides parallel and congruentequilateral triangleregular hexagonparallelogram12.1 Exploring Solids

• Classify three-dimensional figures according to their properties.

Use nets and cross sections to analyze three-dimensional figures. Objectives12.1 Exploring Solids

• faceedgevertexprismcylinderpyramidconecubenetcross sectionVocabulary12.1 Exploring Solids

• 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.12.1 Exploring Solids

• A polyhedron is a solid that is bounded by polygons. 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.12.1 Exploring Solids

• 12.1 Exploring Solids

• A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.12.1 Exploring Solids

• Example 1A: Classifying Three-Dimensional FiguresClassify the figure. Name the vertices, edges, and bases.cubevertices: A, B, C, D, E, F, G, Hbases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF12.1 Exploring Solids

• Example 1B: Classifying Three-Dimensional FiguresClassify the figure. Name the vertices, edges, and bases.pentagonal pyramidvertices: A, B, C, D, E, Fbase: ABCDE 12.1 Exploring Solids

• Check It Out! Example 1a Classify the figure. Name the vertices, edges, and bases.vertex: Nconeedges: nonebase: MM12.1 Exploring Solids

• Check It Out! Example 1b Classify the figure. Name the vertices, edges, and bases.triangular prismbases: TUV, WXYvertices: T, U, V, W, X, Y 12.1 Exploring Solids

• 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.12.1 Exploring Solids

• Example 2A: Identifying a Three-Dimensional Figure From a NetDescribe the three-dimensional figure that can be made from the given net.The net has six congruent square faces. So the net forms a cube. 12.1 Exploring Solids

• Example 2B: Identifying a Three-Dimensional Figure From a NetDescribe the three-dimensional figure that can be made from the given net.The net has one circular face and one semicircular face. These are the base and sloping face of a cone. So the net forms a cone. 12.1 Exploring Solids

• Check It Out! Example 2a Describe the three-dimensional figure that can be made from the given net.The net has four congruent triangular faces. So the net forms a triangular pyramid. 12.1 Exploring Solids

• Check It Out! Example 2b Describe the three-dimensional figure that can be made from the given net.The net has two circular faces and one rectangular face. These are the bases and curved surface of a cylinder. So the net forms a cylinder. 12.1 Exploring Solids

• 12.1 Exploring Solids

• 12.1 Exploring Solids

• 12.1 Exploring Solids

• 12.1 Exploring Solids

• 12.1 Exploring Solids

• A cross section is the intersection of a three-dimensional figure and a plane.12.1 Exploring Solids

• Example 3A: Describing Cross Sections of Three-Dimensional FiguresDescribe the cross section.The cross section is a point. 12.1 Exploring Solids

• Example 3B: Describing Cross Sections of Three-Dimensional FiguresDescribe the cross section.The cross section is a pentagon. 12.1 Exploring Solids

• Check It Out! Example 3a Describe the cross section.The cross section is a hexagon.12.1 Exploring Solids

• Check It Out! Example 3b Describe the cross section.The cross section is a triangle.12.1 Exploring Solids

• Example 4A: Food ApplicationA piece of cheese is a prism with equilateral triangular bases. How can you slice the cheese to make each shape?an equilateral triangle Cut parallel to the bases.12.1 Exploring Solids

• Example 4B: Food ApplicationA piece of cheese is a prism with equilateral triangular bases. How can you slice the cheese to make each shape?a rectangle Cut perpendicular to the bases. 12.1 Exploring Solids

• Check It Out! Example 4 How can a chef cut a cube-shaped watermelon to make slices with triangular faces?Cut through the midpoints of 3 edges that meet at 1 vertex.12.1 Exploring Solids

• Lesson Quiz: Part I1. Classify the figure. Name the vertices, edges, and bases.12.1 Exploring Solids

• 2. Describe the three-dimensional figure that can be made from this net.

square pyramidLesson Quiz: Part II12.1 Exploring Solids

• 3. Describe the cross section.

a rectangleLesson Quiz: Part III12.1 Exploring Solids

• 4. A soccer ball resembles a polyhedron with 32 faces; 20 are regular hexagons and 12 are regular pentagons. How many vertices does this polyhedron have?

Lesson Quiz: Part IV12.1 Exploring Solids

• 12.1 Exploring Solids

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