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Geometry Session 7: Solutions
 
Session 7 Part A Part B Part C Homework
 
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A B C 
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Solutions for Session 7, Part B

See solutions for Problems: B1 | B2 | B3


Problem B1

a. 

For each shape, the center of rotation is the center of the figure. The angles of rotation, from left to right, are 120°, 180°, 120°, and 90°.

b. 

Regular polygons do have rotation symmetry. In each case, the center of rotation is the center of the polygon, and the angle of rotation is 360°/n, where n is the number of sides in the polygon. So the angles are 120°, 90°, 72°, and 60°, respectively, for the equilateral triangle, square, regular pentagon, and regular hexagon.

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Problem B2

The design has no reflection symmetry.

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Problem B3

The final design has three lines of symmetry. Each line of symmetry goes through the center of the rotation symmetry and is a perpendicular bisector of the straight line on the basic design element. Notice that the line symmetry arose because of line symmetry in the original basic design element, something that the first picture lacked.

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