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A mirror design consists of a square mirror with a decorative surround composed of four equilateral triangles, as shown below. We regard two such mirrors as the same if one can be rotated to give the other. A mirror cannot be turned over to give another mirror. (a) Use the Counting Theorem to determine how many different such mirrors can be made if each triangle can be coloured blue, yellow or green. (b) Sketch each of the different such mirrors with exactly two green triangles, one blue triangle and one yellow triangle.

A mirror design consists of a square mirror with a decorative surround composed of four equilateral triangles, as shown below. We regard two such mirrors as the same if one can be rotated to give the other. A mirror cannot be turned over to give another mirror. (a) Use the Counting Theorem to determine how many different such mirrors can be made if each triangle can be coloured blue, yellow or green. (b) Sketch each of the different such mirrors with exactly two green triangles, one blue triangle and one yellow triangle.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A mirror design consists of a square mirror with a decorative surround composed of four equilateral triangles, as shown below. We regard two such mirrors as the same if one can be rotated to give the other. A mirror cannot be turned over to give another mirror. (a) Use the Counting Theorem to determine how many different such mirrors can be made if each triangle can be coloured blue, yellow or green. (b) Sketch each of the different such mirrors with exactly two green triangles, one blue triangle and one yellow triangle.
Transcribed Image Text:A mirror design consists of a square mirror with a decorative surround composed of four equilateral triangles, as shown below. We regard two such mirrors as the same if one can be rotated to give the other. A mirror cannot be turned over to give another mirror. (a) Use the Counting Theorem to determine how many different such mirrors can be made if each triangle can be coloured blue, yellow or green. (b) Sketch each of the different such mirrors with exactly two green triangles, one blue triangle and one yellow triangle.
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