## Introduction:

Parallelograms are an important geometric shape that you may encounter in your math studies. These shapes have unique properties that set them apart from other shapes, and it's important to understand these properties in order to solve problems involving parallelograms. In this article, we will review the properties of parallelograms and provide you with an answer key to some common problems.

## Parallel Sides:

The first property of parallelograms is that opposite sides are parallel. This means that if you extend each side of a parallelogram, they will never intersect. This property is useful in solving problems involving the length of sides and angles of parallelograms.

### Example:

If the length of one side of a parallelogram is 5 units and the opposite side is 8 units, what is the length of the other two sides?

To solve this problem, we can use the fact that opposite sides of a parallelogram are equal in length. Therefore, the length of the other two sides must be 5 units and 8 units respectively.

## Opposite Angles:

The second property of parallelograms is that opposite angles are equal. This means that if you draw a line through the midpoint of a parallelogram, the opposite angles will be congruent. This property is useful in solving problems involving angles of parallelograms.

### Example:

If one angle of a parallelogram measures 60 degrees, what is the measure of the opposite angle?

Since opposite angles of a parallelogram are equal, the measure of the opposite angle must also be 60 degrees.

## Diagonals:

The third property of parallelograms is that the diagonals bisect each other. This means that if you draw the two diagonals of a parallelogram, they will intersect at the midpoint of each diagonal. This property is useful in solving problems involving the length of diagonals and the area of parallelograms.

### Example:

If the length of one diagonal of a parallelogram is 10 units and the length of the other diagonal is 8 units, what is the area of the parallelogram?

To solve this problem, we can use the fact that the diagonals of a parallelogram bisect each other. Therefore, we can divide the parallelogram into two triangles and calculate the area of each triangle. Using the formula for the area of a triangle, we can find that the area of each triangle is 20 square units. Therefore, the total area of the parallelogram is 40 square units.

## Conclusion:

In conclusion, understanding the properties of parallelograms is essential in solving problems involving these shapes. By knowing that opposite sides are parallel, opposite angles are equal, and the diagonals bisect each other, you can easily solve problems involving the length of sides, angles, diagonals, and area of parallelograms. We hope that this review and answer key has been helpful in your math studies.