Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
Mathematical Practices
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Exercise 3 Page 358

Is the set of parallelograms a subset of the set of rectangles?

False, see solution.

Practice makes perfect
We are asked to decide whether the given statement is true or false.

All parallelograms are rectangles. To do so, let's consider the given Venn diagram.

We can see that the set of rectangles is a subset of the set of parallelograms. The set of parallelograms is not a subset of the set of rectangles. Therefore, all rectangles are parallelograms but not all parallelograms are rectangles. The given statement is false.