A parallelogram is a type of quadrilateral whose pairs of opposite sides are parallel.

Quadrilateral ABCD is a parallelogram because AB = DC and AD = BC.

In order to determine whether a quadrilateral is a parallelogram, we will use properties of quadrilaterals.

**If a quadrilateral is a parallelogram, then.**

- Opposite sides are congruent,
- Opposite angles are congruent, and
- Consecutive angles are supplementary.

If one angle of the parallelogram is a right angle, then all the other angles are right angles too. Consider the figure below.

Its given that **J** is a right angle, we can also determine that **L** is a right angle since the opposite sides of parallelograms are congruent. Together, the sum of the measure of those angles is **180** because

We also know that the remaining angles must be congruent because they are also opposite angles.

As per the **Polygon Interior Angles Sum Theorem**, we know that all quadrilaterals have angle measures that add up to **360**. Since **J** and **L** sum up to **180**, we know that the sum of **K** and **M** will also be **180**:

Since **K** and **M** are congruent, we can define their measures with the same variable, **x**. So we have

Therefore, we know that **K** and **M** are both right angles. So, we arrive at

**Example:**

Given that **QRST** is a parallelogram, find the values of **x** and **y** in the diagram below.

**Solution:**

Since opposite sides of parallelograms are congruent, we have set the quantities equal to each other and solve for x:

Now that we've determined that the value of **x** is **7**, we can use this to plug into the expression given in **R**. We know that **R** and **T** are congruent, so we have

Substitute **x** for **7** and we get

So, we've determined that **x=7** and **y=8**.