Square with 4 cm Sides: Determining Rectangle Classification

Square Properties with Rectangle Classification

ABCD is a square with sides measuring 4 cm.


Is ABCD a rectangle?

444AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is ABCD a rectangle?
00:03 In a square, all angles are right angles
00:06 In a square, all pairs of opposite sides are parallel
00:09 Every square is also just a rectangle with equal sides
00:12 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABCD is a square with sides measuring 4 cm.


Is ABCD a rectangle?

444AAABBBDDDCCC

2

Step-by-step solution

We know that the figure shows a square and that, in a square, every pair of opposite sides are parallel.

We also know that every pair of opposite sides in a rectangle are parallel as well.

Therefore, the quadrilateral ABCD is indeed a rectangle.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: A square is always a special type of rectangle
  • Technique: Check if opposite sides are parallel: AB ∥ CD and AC ∥ BD
  • Verification: All squares have four right angles and parallel opposite sides ✓

Common Mistakes

Avoid these frequent errors
  • Thinking squares and rectangles are completely different shapes
    Don't assume squares can't be rectangles because they look different! This leads to wrong classification. Every square meets all rectangle requirements (parallel opposite sides, four right angles). Always remember: all squares ARE rectangles, but not all rectangles are squares.

Practice Quiz

Test your knowledge with interactive questions

It is possible to draw a quadrilateral that is not a rectangle, with the sum of its two adjacent angles equaling 180?

FAQ

Everything you need to know about this question

How can a square be a rectangle if they look different?

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Think of it like this: a square is a special rectangle where all four sides happen to be equal! Just like how a motorcycle is still a vehicle, even though it's different from a car.

What makes something a rectangle?

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A rectangle needs two things: opposite sides must be parallel, and all four angles must be 90°. Since squares have both of these properties, they qualify as rectangles!

Are there other shapes that are also rectangles?

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Yes! Any four-sided shape with parallel opposite sides and four right angles is a rectangle. This includes squares, but also shapes where length ≠ width.

Why is this classification important?

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Understanding that squares are rectangles helps you use rectangle formulas for squares too! Like area = length × width works for both shapes.

What if the problem asks 'Is this rectangle a square?'

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That's the opposite question! Not all rectangles are squares - only rectangles where all four sides are equal can be called squares.

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