Quadrilateral ABCD: Analyzing a 3x6 Shape for Square Properties

Q: What's the difference between a rectangle and a square?

A rectangle has four right angles and opposite sides equal. A square is a special rectangle where all four sides are equal too!

Q: Do I need to check the angles if the sides aren't equal?

No! If the sides aren't all equal, it's automatically not a square. You only need to check angles when all sides are equal first.

Q: How can I remember what makes a square special?

Think of it as the "most perfect" rectangle - it has everything a rectangle has (4 right angles, opposite sides equal) plus all sides are the same length!

Square Properties with Unequal Side Lengths

The quadrilateral ABCD is shown below.

Is ABCD a square?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 quadrilateral ABCD is a square, we need to verify if all sides are equal and if all angles are $90^\circ$ .

1. Given side lengths are $AB = 3$ , $BC = 6$ , $CD = 3$ , and $DA = 6$ . Since all sides are not equal, ABCD cannot be a square.

2. Even without needing to calculate angles, we know that a square requires all four sides to be equal, which they are not. Therefore, this characteristic alone is sufficient to conclude.

Since we determined the side lengths don't match, it logically follows that ABCD is not a square.

Therefore, the solution to the problem is No.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Square Rule: All four sides must be equal length
Technique: Compare opposite sides: AB = 3, CD = 3; BC = 6, DA = 6
Check: Since 3 ≠ 6, not all sides equal, so not a square ✓

Common Mistakes

Avoid these frequent errors

Assuming rectangles are always squares
Don't think every rectangle with right angles is a square = wrong classification! A rectangle only becomes a square when ALL sides are equal, not just opposite sides. Always check that all four sides have the same measurement.

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's the difference between a rectangle and a square?

A rectangle has four right angles and opposite sides equal. A square is a special rectangle where all four sides are equal too!

Do I need to check the angles if the sides aren't equal?

No! If the sides aren't all equal, it's automatically not a square. You only need to check angles when all sides are equal first.

Could this shape be a parallelogram instead?

Yes! Since opposite sides are equal (AB = CD = 3, BC = DA = 6) and the angles appear to be right angles, this is a rectangle - a special type of parallelogram.

What if I measured wrong and the sides were actually equal?

Always double-check your measurements! But based on the given diagram showing $3$ and $6$ , we can trust these values for our analysis.

How can I remember what makes a square special?

Think of it as the "most perfect" rectangle - it has everything a rectangle has (4 right angles, opposite sides equal) plus all sides are the same length!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Square for 9th Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime