Question

The slopes of the sides of a quadrilateral are 2, -1/3, -1/3, and 2. True or false: the quadrilateral is a parallelogram?

1) True
2) False

Answer 1

In this case, the statement "the quadrilateral is a parallelogram" is TRUE.

The answer is option ⇒1) True

Step-by-step explanation:

To determine if the given quadrilateral is a parallelogram, we need to compare the slopes of the opposite sides.

The slopes of the sides are: 2, -1/3, -1/3, and 2.

Let's compare the slopes of the opposite sides:

• 1. The first pair of opposite sides have slopes of 2 and 2. Since these slopes are equal, these sides are parallel.
• 2. The second pair of opposite sides have slopes of -1/3 and -1/3. Again, these slopes are equal, indicating that these sides are parallel as well.

Since both pairs of opposite sides have equal slopes, we can conclude that the quadrilateral with these side slopes is indeed a parallelogram.

Therefore, the statement above is true.

The answer is option ⇒1) True