Question

Which of the following characteristics of a parallelogram leads to the conclusion that every square can always be classified as a parallelogram? Select all that apply.

four equal sides
bisecting diagonals
two pair of opposite parallel sides
two pair of opposite equal angles

Answer 1

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

Answer 2

Bisecting diagonals

Two pair of opposite parallel sides

Two pair of opposite equal angles

Solution:

Let us first define the properties of parallelogram.

• The opposite sides of a parallelogram are parallel.
• The opposite sides of a parallelogram are equal.
• The opposite angles of a parallelogram are equal.
• The diagonals of a parallelogram bisect each other.

Now, let us define the properties of square.

• All four sides of a square are equal.
• Opposite sides of a square are parallel.
• Opposite sides of a square are equal.
• Opposite angles of a square are equal.
• Diagonals bisect each other at 90°.

From these properties, we can conclude that every square can always be classified as a parallelogram if

1. Bisecting diagonals
2. Two pair of opposite parallel sides
3. Two pair of opposite equal angles