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

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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

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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.

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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

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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°

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