Quadrilateral ABCD Analysis: Is a Shape with 6-Unit Sides a Square?

Square Identification with Equal Side Lengths

The quadrilateral ABCD is shown below.

666666666666AAABBBDDDCCC

Is ABCD a square?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The quadrilateral ABCD is shown below.

666666666666AAABBBDDDCCC

Is ABCD a square?

2

Step-by-step solution

The problem requires checking whether quadrilateral ABCDABCD is a square.

  • The quadrilateral is labeled such that each side ABAB, BCBC, CDCD, and DADA is 66, indicating that all sides are of equal length.
  • In geometry, if a quadrilateral has all sides equal and all internal angles as right angles, it is defined as a square.
  • Considering all sides are given as equal, it's logical to presume the angles in this labeled quadrilateral are right angles, a common property when the shape is indeed a square.
  • With both conditions—equal sides and right angles—met, we conclude the figure is a square.

Therefore, the quadrilateral ABCDABCD is a square.

Yes

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Square requires equal sides AND right angles
  • Technique: Check all sides are 6 units and angles are 90°
  • Verification: Count equal sides (4) and right angle markers ✓

Common Mistakes

Avoid these frequent errors
  • Assuming equal sides automatically means square
    Don't think equal sides = square automatically! A rhombus also has equal sides but isn't a square. This leads to wrong classifications of quadrilaterals. Always check that ALL angles are 90° in addition to equal sides.

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 square and a rhombus?

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Both have equal sides, but a square has right angles (90°) while a rhombus can have any angles. The diagram shows right angle markers at each corner, confirming it's a square!

How can I tell if the angles are right angles from the diagram?

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Look for the small square symbols at each corner! These are right angle markers that indicate 90° angles. Without these markers, you can't assume the angles are right angles.

Could this be a rectangle instead of a square?

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No! A rectangle has opposite sides equal, but this shape has all four sides equal to 6. Since it also has right angles, it must be a square (which is a special type of rectangle).

What if I only see that all sides are 6 units?

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Equal sides alone aren't enough! You need to check for right angle markers too. In this diagram, you can see the small squares at each vertex indicating 90° angles.

Are all squares also rectangles?

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Yes! A square is a special rectangle where all sides are equal. Every square has the properties of a rectangle (opposite sides parallel, all angles 90°) plus equal sides.

What makes this definitely a square and not just any quadrilateral?

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Three key features: (1) All four sides equal 6 units, (2) Right angle markers at all corners, and (3) Opposite sides are parallel. These properties together define a square.

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