## Introduction

If you are studying geometry, you might have come across the term "parallelogram" which is a four-sided shape. In this article, we will discuss the properties of parallelograms answer key 6-2. We will cover the definition of parallelograms, their properties, and how to solve problems related to parallelograms.

## What is a Parallelogram?

A parallelogram is a four-sided shape with opposite sides that are parallel and congruent. This means that opposite sides of the parallelogram are equal in length and do not intersect. The opposite angles of the parallelogram are also equal in measure.

## Properties of Parallelograms

There are several properties of parallelograms that you should know:

### 1. Opposite Sides are Parallel and Congruent

As mentioned earlier, opposite sides of a parallelogram are parallel and congruent. This property makes it easier to solve problems related to parallelograms. If you know the length of one side, you can easily find the length of the opposite side.

### 2. Opposite Angles are Equal

The opposite angles of a parallelogram are equal in measure. This means that if one angle is 60 degrees, the opposite angle will also be 60 degrees. This property is useful when you need to find the measure of one angle and you already know the measure of the opposite angle.

### 3. Consecutive Angles are Supplementary

Consecutive angles of a parallelogram are supplementary. This means that if one angle is 60 degrees, the next angle will be 120 degrees. This property is useful when you need to find the measure of one angle and you already know the measure of the consecutive angle.

### 4. Diagonals Bisect Each Other

The diagonals of a parallelogram bisect each other. This means that the point where the diagonals intersect divides each diagonal into two congruent segments. This property is useful when you need to find the length of one diagonal and you already know the length of the other diagonal.

## Solving Problems Related to Parallelograms

To solve problems related to parallelograms, you need to use the properties mentioned above. You can use formulas to find the length of sides or angles. Here are some examples:

### Example 1

Find the length of side AB in the parallelogram below. Solution: Since opposite sides of a parallelogram are congruent, we know that AB = DC. Therefore, AB = 7cm.

### Example 2

Find the measure of angle A in the parallelogram below. Solution: Since opposite angles of a parallelogram are equal, we know that angle A = angle C. Therefore, angle A = 100 degrees.

### Example 3

Find the length of diagonal AC in the parallelogram below. Solution: Since the diagonals of a parallelogram bisect each other, we know that AC = 2x. We also know that BD = 10cm. Using the Pythagorean theorem, we can find x: x^2 + 6^2 = 10^2 x^2 + 36 = 100 x^2 = 64 x = 8 Therefore, AC = 2x = 16cm.

## Conclusion

In conclusion, parallelograms have several properties that make them easier to work with. Opposite sides are parallel and congruent, opposite angles are equal, consecutive angles are supplementary, and diagonals bisect each other. By using these properties, you can solve problems related to parallelograms.

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