Quadrilateral ABCD: Verifying Square Properties with 8 and 5 Unit Measurements

The quadrilateral ABCD is shown below.

Is ABCD a square?

To determine if the quadrilateral ABCD is a square, we must check the properties of a square. A square requires all four sides to have equal lengths and all interior angles to be $90^\circ$.

• Step 1: Identify the given side lengths.

• Step 2: Compare the side lengths.

• Step 3: Evaluate the conclusion based on side length comparison.

Step 1: The diagram provides us with the following side lengths:

• AB = 8

• BC = 5

Step 2: Compare the given sides.

The side AB is labeled with a length of 8, while the vertical side BC is labeled 5. For ABCD to be a square, all sides would need to be the same length.

Step 3: Evaluation.

Since two adjacent sides AB and BC have different lengths (AB = 8 and BC = 5), it is evident that not all sides are equal.

As a result, we can conclude that ABCD cannot be a square because the sides are not all the same length.

Therefore, the quadrilateral ABCD is not a square.