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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Refer to the pyramids of Exercises 3 and 4. Which of these have symmetry with respect to one (or more) plane(s)?

To determine

To find:

The pyramid that has symmetry with respect to one (or more) plane(s).

Explanation

Given:

The prism from Exercise given below

3. a)

and lateral faces are congruent; base is a square.

3. b)

and base is a square.

4. a)

and lateral faces are congruent; base is a regular polygon.

4. b)

and lateral faces are not congruent.

Properties Used:

Symmetry is when two or more parts are identical after a flip, slide or turn. A plane of symmetry is an imaginary plane along which the figure is flipped, slides or turned to get two or more identical parts.

To have this type of symmetry, a plane can be drawn for which each point of the space figure has a corresponding point on the opposite side of the plane at the same distance from the plane as shown in figure below

Calculation:

In the figure (3a) given below

draw a plane by joining the apex and the midpoints of opposite sides of the square base

Since, each point of the space figure has a corresponding point on the opposite side of the plane at the same distance from the plane. Hence, it has symmetry with respect to one (or more) plane(s).

In the figure (3b) given below

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