Holt 10.1 Practice A

Name Date Class

LESSON Practice A 10-1 Solid Geometry

For Exercises 1–4, match the given parts of the figure to the names. 5 1. vertex a. triangle PUT 2. edge b. point T 3. face c. pentagon PQRST 4 3 0 2 4. base d. segment PU 1 Classify each figure. Name the vertices, edges, and bases. & 5. 6.

$ % $ % #

! " Type of figure: Type of figure:

Vertices: Vertices:

Edges: Edges:

Bases: Bases:

Tell what kind of three-dimensional figure can be made from the given net. 7. 8.

Tell what kind of shape each cross section makes. 9. 10.

IN 11. Soren cut several edges of a cereal box and then unfolded the box IN so it looks like this. Draw the box as it originally appeared and label IN the side lengths. IN

For Exercises 1–4, match the given parts of the figure to the names. 5 Classify each figure. Name the vertices, edges, and bases. ' 9 1. vertex b a. triangle PUT 1. 2. 2. edge d b. point T 3. face a or c c. pentagon PQRST 4 3 0 2 & % 4. base c d. segment PU ! $ 1 : Classify each figure. Name the vertices, edges, and bases. " # & hexagonal pyramid cone 5. 6. $ % vertices: A, B, C, D, E, F, and G vertices: Y $ % _ _ _ _ _ # edges: AB , BC, CD , DE, EF, edges: none ______! " FA , AG,BG, CG, DG , EG, FG Type of figure: cylinder Type of figure: triangular prism base: hexagon ABCDEF base: (Z Vertices: none Vertices: A, B, C, D, E, and F _ _ _ _ Name the type of solid each object is and sketch an example. Edges: none Edges: AB , AC, BC , AD, _ _ _ _ _ 3. a shoe box 4. a can of tuna BE, CF, DE, DF, and EF

Bases: (D and (E Bases: nABC and nDEF rectangular prism cylinder Tell what kind of three-dimensional figure can be made from the given net. 7. 8. Describe the three-dimensional figure that can be made from the given net. 5. 6.

rectangular prism rectangular pyramid Tell what kind of shape each cross section makes. cylinder hexagonal prism 9. 10. 7. Two of the nets below make the same solid. Tell which one does not. III

I II III Describe each cross section. triangle rectangle 8. 9. IN 11. Soren cut several edges of a cereal box and then unfolded the box IN so it looks like this. Draw the box as it originally appeared and label IN the side lengths. circle rectangle Possible answer: IN 15 in. 10. After completing Exercises 8 and 9, Lloyd makes a conjecture about the shape of any IN cross section parallel to the base of a solid. Write your own conjecture. Possible answer: If a cross section intersects a solid parallel to a base, 9 in. 3 in. then the cross section has the same shape as the base.

LESSON Practice C LESSON Review for Mastery 10-1 Solid Geometry 10-1 Solid Geometry A sphere is a three-dimensional figure bounded by all the points a fixed distance Three-dimensional figures, An edge is the from a central point. Examples of a sphere include a globe and a basketball. or solids, can have flat or segment where two 1. Name the two possible geometric figures that can result from the intersection of curved surfaces. faces intersect. a plane and a sphere. Prisms and pyramids are Each flat a circle or a point named by the shapes of surface is A vertex is the point where their bases. called a three or more faces intersect. In 2. Tell whether a sphere has vertices, edges, faces, or bases. Name the two things face. a cone, it is where the curved that define a sphere. surface comes to a point. Possible answer: No, a sphere has no vertices, edges, faces, or bases. Solids A point (center) and a radius (distance) define a sphere. Prisms Pyramids Cylinder Cone

vertex A conic section is the intersection of a plane and a cone (or double cone). Many 2 2 bases conic sections can be modeled by equations in x, y, x , and y . First graph each bases bases base equation. Then sketch a plane and a cone so that their intersection has the same shape as the graph of the equation. (Hint: Sketch a double cone in Exercise 7.) triangular rectangular triangular rectangular Neither cylinders nor cones 2 3. y 5 x Y 4. y 5 x Y prism prism pyramid pyramid have edges.

X Classify each figure. Name the vertices, edges, and bases. X 1. R 2. A

2 2 2 2 y 5. x 1 y 5 9 Y 6. _x_ 1 __ 5 1 Y S 4 9 B Q T X X triangular pyramid; vertices: Q, R, cylinder; vertices: none; _ _ _ _ _ S, T; edges: QR , QS , QT , RS , ST , edges: none; bases: (A, (B _ TR ; base: nQST 7. y 2 2 x 2 5 1 (Hint: Remember that y 2 5 1 has two solutions.) 3. G 4. L Y D F H C E M X triangular prism; vertices: C, D, E, F, cone; vertex: M; edges: none; ______G, H; edges: C D , D E , E C , FG, G H , HF , base: (L _ _ _ CF , DG , EH ; bases: nCDE, nFGH