7-6 Cross Sections Identify the figure. Then name the bases, faces, edges, and vertices. Then, Identify a pair of skew lines. 1. Figure name: bases: faces: edges: vertices: skew lines: SOLUTION: Figure name: The figure has one triangular base and sides that are all triangles. The figure is a triangular pyramid. bases: ACD faces: ACD, ABD, ABC, DBC edges: , , , , , vertices: A, B, C, D skew lines: Sample answer: and ANSWER: Figure name: triangular pyramid bases: ACD faces: ACD, ABD, ABC, DBC edges: , , , , , vertices: A, B, C, D skew lines: Sample answer: and Describe the shape resulting from the cross section. 3. SOLUTION: The cross section is a rectangle. ANSWER: rectangle eSolutions Manual - Powered by Cognero Page 1 7-6 Cross Sections 5. SOLUTION: The cross section is a triangle. ANSWER: triangle 7. Use a Counterexample State whether the following conjecture is true or false. If false, provide a counterexample. Two planes in three-dimensional space can intersect at one point. SOLUTION: False; two planes intersect at a line, which is an infinite number of points. ANSWER: False; two planes intersect at a line, which is an infinite number of points. 9. Model with Mathematics Draw the cross sections of a polyhedron, cylinder, or cone. Exchange papers with another student. Identify the three-dimensional figures represented by the cross sections. SOLUTION: See students' work. ANSWER: See students' work. Persevere with Problems Determine whether the statement is always, sometimes, or never true. Explain your reasoning. 11. A prism has 2 bases and 4 faces. SOLUTION: Sometimes; a rectangular prism has 2 bases and 4 faces, but a triangular prism has 2 bases and 3 faces. ANSWER: Sometimes; a rectangular prism has 2 bases and 4 faces, but a triangular prism has 2 bases and 3 faces. 13. A pyramid has a rectangular base. SOLUTION: sometimes; A triangular pyramid has a triangle for its base. ANSWER: sometimes; A triangular pyramid has a triangle for its base. eSolutions Manual - Powered by Cognero Page 2 7-6 Cross Sections Identify the figure. Then name the bases, faces, edges, and vertices. Then identify a pair of skew lines. 15. Figure name: bases: faces: edges: vertices: skew lines: SOLUTION: Figure name: rectangular prism bases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF faces: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF edges: , , , , , , , , , , , vertices: A, B, C, D, E, F, G, H skew lines: and ANSWER: Figure name: rectangular prism bases: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF faces: ABCD, EFGH, ABFE, DCGH, ADHE, BCGF edges: , , , , , , , , , , , vertices: A, B, C, D, E, F, G, H skew lines: and Describe the shape resulting from the cross section. 17. SOLUTION: The cross section is a curve. ANSWER: curve eSolutions Manual - Powered by Cognero Page 3 7-6 Cross Sections 19. Find the Error Hannah is identifying the figure below. Find her mistake and correct it. SOLUTION: Because there are two parallel, congruent triangular bases, it is a triangular prism. A triangular pyramid has one base that is a triangle and sides that are in the shape of triangles. ANSWER: Because there are two parallel, congruent triangular bases, it is a triangular prism. eSolutions Manual - Powered by Cognero Page 4 7-6 Cross Sections 21. Match each number of faces, edges, and vertices to the correct solid figure. a. 4 faces, 6 edges, 4 vertices ____________ b. 5 faces, 8 edges, 5 vertices ____________ c. 5 faces, 9 edges, 6 vertices ____________ SOLUTION: Count the number of faces, edges, and vertices in each figure, and match those up with the choices: a. 4 faces, 6 edges, 4 vertices: Figure 2 b. 5 faces, 8 edges, 5 vertices: Figure 1 c. 5 faces, 9 edges, 6 vertices: Figure 3 ANSWER: a. Figure 2 b. Figure 1 c. Figure 3 Name the polygon. 23. SOLUTION: The polygon has six sides. So, the polygon is a hexagon. ANSWER: hexagon eSolutions Manual - Powered by Cognero Page 5 7-6 Cross Sections 25. Find the measure of the missing angle of the polygon. SOLUTION: The figure shown is a rectangle. A rectangle is a polygon with 4 right angles and a right angle measures 90°. So, the missing angle of the rectangle is 90°. ANSWER: 90° eSolutions Manual - Powered by Cognero Page 6.