   Chapter 9.2, Problem 17E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section 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 a line?

To determine

To find:

The pyramid that has symmetry with respect to a line.

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 line of symmetry is an imaginary line along which the figure is flipped, slides or turned to get two or more identical parts.

To have this type of symmetry, a line can be drawn such that every point of the figure has a corresponding point directly opposite and at the same distance from the line as shown in figure below

Line symmetry can also be described as reflection symmetry i.e. if you fold the figure along the line, then both the sides overlap.

Calculation:

In the figure (3a) given below

draw a line by joining the apex and the center of the square base such that if it is folded along this line both sides overlap

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