Determine If the Quadrilateral is a Square: Analyzing Side and Angle Properties

Question

Look at the quadrilateral below.

AAABBBDDDCCC

Is the quadrilateral a square?

Step-by-Step Solution

To determine if the quadrilateral is a square, we need to verify the defining characteristics of a square:

  • All four sides must be of equal length.
  • Each of the four angles must be a right angle (9090^\circ).
  • The diagonals should be equal and bisect each other at right angles.

From the problem description and the diagram provided:

  • The quadrilateral is labeled ABCD, and the diagram shows right angles at each corner (A=B=C=D=90 \angle A = \angle B = \angle C = \angle D = 90^\circ).
  • Visual inspection of the diagram suggests the sides AB, BC, CD, and DA appear equal, conforming to the property that all sides of a square are equal. This is inferred based on the symmetry and right angles in the diagram.
  • Furthermore, the diagonals AC and BD in the diagram intersect at right angles, suggesting they are equal and bisect each other, which is a characteristic property of a square.

Therefore, checking all the conditions:

  • Equal sides — based on the diagram.
  • Right angles at each vertex — confirmed as all angles are labeled 9090^\circ.
  • Equal and bisected diagonals — inferred from the intersection and right angles.

Conclusively, the quadrilateral satisfies all the characteristics of a square. Thus, the given quadrilateral is indeed a square.

Yes, the shape is a square.

Answer

Yes


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