Geometry Session 3: Solutions

A B C
Homework

Solutions for Session 3, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6

Problem B1

symmetry

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Problem B2

See the diagram below. Note that shapes e, f, h, j, and m are neither triangular, regular, nor concave, so they belong outside all three circles of the diagram.

3 circles

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Problem B3

a.

b.

c.

d.

e.

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Problem B4

a.	Label 1 is Irregular, Label 2 is Regular, and Label 3 is Pentagon.
b.	The overlap would have to contain polygons that are simultaneously regular and irregular. No such polygons exist!
c.	Every pentagon is either regular or irregular. For there to be a polygon in the Label 3 circle but not in any others, there would have to be a pentagon which is neither regular nor irregular. This is impossible.

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Problem B5

Answers will vary. One possibility is to label the regions Triangle, Quadrilateral, and Pentagon.

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Problem B6

Answers will vary. One possibility is Not Triangle, Not Quadrilateral, and Not Hexagon. Even if a shape is one of those three things, it's sure to not be the other two, so every shape is in the overlap of two circles, and some (pentagons) are in the overlap of all three.

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Session 3 | Notes | Solutions | Video