Quadrilateral ABCD: Verify if a 7x8 Shape is a Square

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

A square is a special type of rectangle where all four sides are equal. Every square is a rectangle, but not every rectangle is a square. Think of it like this: rectangle + equal sides = square.

Q: If the shape has right angles, why isn't it a square?

Having right angles makes it a rectangle, but to be a square, you need both right angles AND all sides equal. This shape has sides of 7 and 8, so it's a rectangle but not a square.

Q: What if I'm given a shape that looks square but has different measurements?

Always trust the measurements! Visual appearance can be deceiving. If the measurements show unequal sides (like 7 and 8), then it's definitely not a square, regardless of how it looks.

Q: Could this shape still be called a quadrilateral?

Yes! A quadrilateral is any four-sided shape. This 7×8 rectangle is still a quadrilateral - just not a square. The hierarchy goes: quadrilateral → rectangle → square (each getting more specific).

Square Properties with Unequal Dimensions

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

As we see that BD is equal to 8 and AC is equal to 7, the sides are not equal, and this contradicts the properties of the square, where all sides are equal to each other, therefore the quadrilateral is not a square

Final Answer

Key Points to Remember

Essential concepts to master this topic

Square Definition: All four sides must be equal in length
Analysis Method: Compare given dimensions: 7 ≠ 8, so not equal
Verification: Check if all sides match: 7, 8, 7, 8 shows inequality ✓

Common Mistakes

Avoid these frequent errors

Assuming rectangles are always squares
Don't think that any four-sided shape with right angles is automatically a square = wrong classification! Rectangles can have different length and width. Always check that ALL four sides are equal, not just that angles are 90°.

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 square is a special type of rectangle where all four sides are equal. Every square is a rectangle, but not every rectangle is a square. Think of it like this: rectangle + equal sides = square.

If the shape has right angles, why isn't it a square?

Having right angles makes it a rectangle, but to be a square, you need both right angles AND all sides equal. This shape has sides of 7 and 8, so it's a rectangle but not a square.

How do I quickly identify a square?

Check two things: 1) All angles are 90° (right angles), and 2) All four sides are the same length. If either condition fails, it's not a square.

What if I'm given a shape that looks square but has different measurements?

Always trust the measurements! Visual appearance can be deceiving. If the measurements show unequal sides (like 7 and 8), then it's definitely not a square, regardless of how it looks.

Could this shape still be called a quadrilateral?

Yes! A quadrilateral is any four-sided shape. This 7×8 rectangle is still a quadrilateral - just not a square. The hierarchy goes: quadrilateral → rectangle → square (each getting more specific).

🌟 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