We've saved the simplest figures for last: rectangles and squares. Here are the definitions.

Rectangle: A rectangle is a parallelogram in which each interior angle is 90 degrees.

Square: A square is a rhombus in which each interior angle is 90 degrees.

There are other ways of defining these two figures; we could say that a rectangle is a parallelogram with adjacent angles congruent, or we could say that a square is a rhombus with adjacent angles congruent. But I think the definitions I've given are the simplest.

Since a rectangle is a parallelogram, and a parallelogram is a quadrilateral, all the properties of quadrilaterals and parallelograms apply to rectangles.

Since a square is a rhombus, and a rhombus is a parallelogram, and a parallelogram is a quadrilateral, all the properties of quadrilaterals, parallelograms and rhombuses apply to squares.

Also, it should be noted that, just as some parallelograms are rhombuses, some rectangles are squares. Some folks think that rectangles can't be squares, but that's not true unless you change the definition of a rectangle to specify that the sides can't all be the same length.

What are the special properties of rectangles and squares? Well, since the angles of both rectangles and squares are 90 degrees, we can always use the Pythagorean Theorem to find the lengths of the diagonals.

Also, since the sides are perpendicular, you can treat any side as the base, and an adjacent side as the altitude, to get the area.

A_r = bh

A_s = s²

1.

Which is true: "All parallelograms are rectangles," or "All rectangles are parallelograms."

2.

True or false: All squares are rectangles

3.

True or false: All rectangles are squares

4.

True or false: All squares are parallelograms

5.

The area of a square is 36 square units. What is the length of a side?

6.

If the sides of a rectangle are 5 and 12, what is the length of a diagonal?

7.

The area of a rectangle is 48 square units, and one side has length 12 units. What is the other side length?

8.

Are any trapezoids rectangles? Why or why not?

9.

The area of a rectangle is 36 square units, and its perimeter is 26. What are the lengths of the sides?

10.

The area of a square is one half its perimeter. What is the length of a side?