Question

list the quadrilaterals that have the given property. choose among parallelogram, rhombus, rectangle, and square.

all sides are \\(\cong\\).

choose the correct answer below.

a. square only
b. rhombus and square only
c. parallelogram, rectangle, rhombus, and square
d. rectangle and square only

Explanation:

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<reasoning>

Analyze the given property

The property is "All sides are \(\cong\)" (all sides are congruent/equal in length).

Evaluate the candidate quadrilaterals

• Parallelogram: Opposite sides are congruent, but all four sides do not have to be congruent.
• Rhombus: By definition, a rhombus is a quadrilateral with four congruent sides.
• Rectangle: Opposite sides are congruent, but all four sides do not have to be congruent.
• Square: By definition, a square is a regular quadrilateral, meaning it has four congruent sides and four right angles.

Determine the correct option

The quadrilaterals that have all sides congruent are the rhombus and the square. This corresponds to option B.
</reasoning>

<answer>
<mcq-option>(A) Square only</mcq-option>
<mcq-correct>(B) Rhombus and square only</mcq-correct>
<mcq-option>(C) Parallelogram, rectangle, rhombus, and square</mcq-option>
<mcq-option>(D) Rectangle and square only</mcq-option>
</answer>

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Answer:

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<reasoning>

Analyze the given property

The property is "All sides are \(\cong\)" (all sides are congruent/equal in length).

Evaluate the candidate quadrilaterals

• Parallelogram: Opposite sides are congruent, but all four sides do not have to be congruent.
• Rhombus: By definition, a rhombus is a quadrilateral with four congruent sides.
• Rectangle: Opposite sides are congruent, but all four sides do not have to be congruent.
• Square: By definition, a square is a regular quadrilateral, meaning it has four congruent sides and four right angles.

Determine the correct option

The quadrilaterals that have all sides congruent are the rhombus and the square. This corresponds to option B.
</reasoning>

<answer>
<mcq-option>(A) Square only</mcq-option>
<mcq-correct>(B) Rhombus and square only</mcq-correct>
<mcq-option>(C) Parallelogram, rectangle, rhombus, and square</mcq-option>
<mcq-option>(D) Rectangle and square only</mcq-option>
</answer>

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