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Question
Choose ALL answers that describe the polygon if ,
, and .
Answer Atemptiout of 2
Parallelogramples
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid

Ask by Mitchell Knight. in the United States
Jan 24,2025

Solución de inteligencia artificial de Upstudy

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The polygon is a rhombus and a quadrilateral.

Solución

To analyze the polygon based on the given conditions, let’s break down the information step by step:
  1. Sides of the Polygon:
    • We know that , , , and . This means all sides of the polygon are equal, indicating that it is a rhombus or a square.
  2. Angles of the Polygon:
    • The conditions state that and . This suggests that the opposite angles are equal.
  3. Types of Quadrilaterals:
    • A parallelogram has opposite sides that are equal and opposite angles that are equal.
    • A rectangle has all angles equal to and opposite sides equal.
    • A rhombus has all sides equal and opposite angles equal.
    • A square is a special case of both a rectangle and a rhombus, where all sides are equal and all angles are .
    • A trapezoid has at least one pair of parallel sides, which is not indicated here.
  4. Conclusion:
    • Since all sides are equal and opposite angles are equal, is at least a rhombus.
    • If the angles and are , then it would also be a rectangle and thus a square. However, we do not have information confirming that the angles are .
Based on this analysis, the polygon can be classified as:
  • Rhombus (since all sides are equal and opposite angles are equal)
  • Quadrilateral (since it has four sides)
The other options (parallelogram, rectangle, square, and trapezoid) cannot be definitively concluded without additional information about the angles.

Final Answers:

  • Rhombus
  • Quadrilateral

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Beyond the Answer

The polygon is a quadrilateral since it has four sides. Given that all sides are equal ( ), this indicates that it’s not just any quadrilateral but a special type known as a rhombus! Since the angles and , it confirms the symmetrical properties of a rhombus, but without further information on the angles being right angles, it can’t be established as a square.
Another fun fact is that a rhombus is essentially a “superhero” version of a parallelogram. While all rhombuses (like our polygon) are parallelograms due to their opposite sides being equal and parallel, only a short leap is needed to find them transforming into a rectangle if the angles are right! So, if you know your shapes, you now know is a rhombus and a special quadrilateral.

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