Square Properties: Analyzing a Quadrilateral with 3-Unit Sides

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

Both have four equal sides, but only a square has four right angles (90°). A rhombus can have any angle measures as long as opposite angles are equal.

Q: How can I tell if the angles are 90° from the diagram?

Look for small square symbols at each corner! These indicate right angles. In this problem, you can see small squares at vertices A, B, C, and D.

Q: Are all rectangles squares?

No! All squares are rectangles (4 right angles), but rectangles only become squares when all four sides are equal length.

Q: What if I only know that opposite sides are equal?

That describes a rectangle, not necessarily a square. For a square, you need all four sides equal plus all four angles at 90°.

Square Identification with Equal Sides

ABCD is a quadrilateral.

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

ABCD is a quadrilateral.

Is ABCD a square?

Step-by-step solution

To determine if the quadrilateral ABCD is a square, we must confirm two simple properties: all sides are equal, and all angles are right angles.

According to the problem, ABCD is a quadrilateral where all sides denoted by $\overline{AB} = \overline{BC} = \overline{CD} = \overline{DA} = 3$ . This indicates that all sides are equal.

Visual context and information suggest, despite angles not being numerically specified, that the shape illustrates a square. Typically, when all sides are equal and we assume connecting lines that meet perpendicularly (which a standard square depiction strongly suggests), the angles are $90^{\circ}$ .

Therefore, since all sides are equal and it is reasonable to expect all angles are right angles from the context provided, ABCD satisfies the conditions for being a square.

Thus, the quadrilateral ABCD is a square, so the correct answer is "Yes".

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Square Properties: All four sides equal AND all four angles are 90°
Visual Analysis: Corner squares in diagram indicate right angles at each vertex
Verification: Check both equal sides (3 units each) and right angle markers ✓

Common Mistakes

Avoid these frequent errors

Assuming equal sides automatically make a square
Don't think that just having four equal sides = square! A rhombus also has four equal sides but isn't a square. Always verify that all angles are 90° too by looking for right angle markers or perpendicular indicators.

Practice Quiz

Test your knowledge with interactive questions

Is a square a trapezoid?

FAQ

Everything you need to know about this question

What's the difference between a square and a rhombus?

Both have four equal sides, but only a square has four right angles (90°). A rhombus can have any angle measures as long as opposite angles are equal.

How can I tell if the angles are 90° from the diagram?

Look for small square symbols at each corner! These indicate right angles. In this problem, you can see small squares at vertices A, B, C, and D.

Are all rectangles squares?

No! All squares are rectangles (4 right angles), but rectangles only become squares when all four sides are equal length.

What if I only know that opposite sides are equal?

That describes a rectangle, not necessarily a square. For a square, you need all four sides equal plus all four angles at 90°.

Can I use the Pythagorean theorem to check if it's a square?

Yes! In a square with side length 3, the diagonal should equal $3\sqrt{2}$ . If $3^2 + 3^2 = d^2$ , then $d = 3\sqrt{2} \approx 4.24$ .

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