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

Q: What if only two sides are labeled but the shape looks square?

You can only work with the given information. If two adjacent sides have different lengths (like 8 and 5), then it's definitely not a square, regardless of how it looks.

Q: Could this be a rectangle instead?

Yes! A rectangle only requires opposite sides to be equal and all angles to be $ 90^\circ $. Since AB = 8 and BC = 5, this could be a rectangle with opposite sides equal.

Q: What if the diagram is just not drawn to scale?

Always trust the numerical measurements over the visual appearance. Mathematical diagrams often aren't drawn to scale, so the given numbers (8 and 5) are the reliable information.

Q: How many sides do I need to check for a square?

Technically, you only need to find two adjacent sides that are different lengths. Once you know AB ≠ BC, you can immediately conclude it's not a square!

Q: What makes this problem tricky?

The quadrilateral looks like it could be a square in the diagram, but the measurements tell the real story. This teaches you to rely on given data rather than visual impressions.

Square Properties with Unequal Side Lengths

The quadrilateral ABCD is shown below.

Is ABCD a square?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The quadrilateral ABCD is shown below.

Is ABCD a square?

Step-by-step solution

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.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Square Definition: All four sides must be equal and all angles $90^\circ$
Technique: Compare given measurements: AB = 8 ≠ BC = 5
Check: If any two sides differ, it cannot be a square ✓

Common Mistakes

Avoid these frequent errors

Assuming a quadrilateral is a square based on appearance alone
Don't just look at the shape and assume it's a square because it looks rectangular = wrong conclusion! Visual appearance can be misleading without exact measurements. Always compare all given side lengths and verify they are equal.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

Is a parallelogram a square?

FAQ

Everything you need to know about this question

What if only two sides are labeled but the shape looks square?

You can only work with the given information. If two adjacent sides have different lengths (like 8 and 5), then it's definitely not a square, regardless of how it looks.

Could this be a rectangle instead?

Yes! A rectangle only requires opposite sides to be equal and all angles to be $90^\circ$ . Since AB = 8 and BC = 5, this could be a rectangle with opposite sides equal.

What if the diagram is just not drawn to scale?

Always trust the numerical measurements over the visual appearance. Mathematical diagrams often aren't drawn to scale, so the given numbers (8 and 5) are the reliable information.

How many sides do I need to check for a square?

Technically, you only need to find two adjacent sides that are different lengths. Once you know AB ≠ BC, you can immediately conclude it's not a square!

What makes this problem tricky?

The quadrilateral looks like it could be a square in the diagram, but the measurements tell the real story. This teaches you to rely on given data rather than visual impressions.

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