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Exam 18: Symmetry

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Question 1

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Consider the following right regular hexagonal prism. A) How many reflection symmetries does the figure have? B) How many rotational symmetries does the figure have?

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Question 2

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Add to the picture so that it has a reflection symmetry. Draw in the line symmetry.

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Question 3

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A) How many rotational symmetries does a regular 12-gon have? B) What is the minimum (positive) number of degrees of rotation for the symmetry of a regular 12-gon?

How many reflection symmetries does a regular hexagon have? Draw the hexagon and show all the lines of symmetry.

How many reflection and rotational symmetries does a regular octagon have?

Describe all of the reflection and rotational symmetries of the following three-dimensional object. (Feel free to draw pictures to demonstrate.) All of the angles in the object are 90°.

A circle has exactly 360 rotational symmetries.

Add to following figure so that it has rotational symmetry. Show a center of rotation after the addition.

For each figure, draw in all lines of reflection symmetry. If the figure has no lines of symmetry, write "none." A) B) C)

Determine the SMALLEST positive amount of the turn (in degrees) for the rotational symmetries in each figure. A) B) C)

The polyhedron below has exactly one plane of reflection symmetry and one line of rotational symmetry.

A) Add to the following design so that it has a reflection symmetry. Draw in the line of symmetry. B) Now add to the original design so that it has a rotational symmetry. Show the center of rotation.

A) How many reflection symmetries does the figure below have? B) How many rotational symmetries does it have?

Add to the picture so that it has a rotational symmetry. Show the center of rotation.

Complete the following sentences. A) A regular 90-gon has a total of _____ rotational symmetries. B) A regular 90-gon has a total of _____ reflection symmetries. C) The smallest positive rotational symmetry of a regular 90-gon would have _____ degrees.

Sketch a regular triangle and mark all lines of reflection symmetry.

A) How many reflection symmetries does every right prism have if its bases are rectangles that are not squares? B) How many rotational symmetries does every regular square pyramid have?