Question

Choose ALL answers that describe the polygon VWXY if VW = 10, WX = 10, XY = 10,

YV = 10, and m/V = m/W = m/X = m/Y.
Answer Attempt 1 out of 2
Parallelogram
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid

Answer 1

The polygon VWXY with equal sides and angles is a square, which is a specific type of quadrilateral. It is not necessary to call it by other names such as parallelogram or trapezoid as square defines it fully.

Step-by-step explanation:

The polygon VWXY can be described based on the given lengths and angles. Since VW = WX = XY = YV = 10, we know that all four sides are equal. Additionally, the problem states that m/V = m/W = m/X = m/Y, which indicates all angles are equal. If a four-sided polygon has all sides equal and all angles equal, it is a square. Therefore, the polygon VWXY is a square.

This also means the square is a quadrilateral since that term describes any four-sided polygon. However, while all squares are rectangles and rhombuses due to their specific properties (all angles are 90 degrees and all sides are equal), calling it a rectangle or rhombus would be less precise. We do not typically refer to squares as parallelograms or trapezoids, though technically, squares fit the definition of parallelograms. Nevertheless, since square is the most specific term available and fully describes the polygon, other terms are generally not necessary.