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Geometric Sense
Lesson 11		 Properties and Relationships
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 > Practice: 1 | 2 | 3 | 4 | 5 > Reflection

Example 3:

Which of the following statements are true?

  1. All rectangles are squares.
  2. All squares are rectangles.
  3. No square is a rectangle.
  4. No rectangle is a square.
Explain in detail how you found your answer using words, numbers, and/or pictures. (2 point response)

In order to receive the 2 points for this problem, make sure that you do the following:

  • For 1 point answer the question. State which of the statements are true. You may either identify them by the letter before the statement or the statement itself.
  • For the other 1 point, you need to explain your answer supporting your answer in detail.

Let's begin by solving and working out the statements to see which statements are true. With this work you are building up your support for your eventual choice(s).

  • Statement A, all rectangles are squares is false. By definition of a rectangle, the figure needs to have 4 sides and the opposite sides need to be equal. A square is a kind of rectangle. Therefore, statement A isn't one of the true responses.
  • Statement B, all squares are rectangles is true. Since by definition squares are a kind of rectangle, you know that all squares are rectangles. Every square has 4 sides and its opposite sides are equal so therefore is always a rectangle. So you know statement B is true.
  • Statement C, no square is a rectangle is false. As you stated previously, a square is a kind of a rectangle so this statement cannot be true as every square is a rectangle.
  • Statement D, no rectangle is a square is false also. You do know that there are some rectangles that are squares since squares are a type of rectangle.

As you look back over your choices and what you found out, you notice that the only correct choice is statement B, all squares are rectangles. To receive the two points for the problem your answer may look something like this.

The only true statement is B, all squares are rectangles. The reason that this statement is true is because the meaning of a rectangle is a parallelogram with 4 right angles and a square is a parallelogram with 4 right angles and all 4 sides the same length. For rectangles the opposite sides need to be the same length, but all 4 sides don't have to be the same length. Therefore a square is just a certain kind of a rectangle.

Practice 1 >>

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