Tony has a piece of wire 36 inches long. He bent it into a quadrilateral with sides of equal length and angles of equal measure.

(Part A)
Classify the quadrilateral. Give all the names that fit.

(Part B)
Justify your answer with evidence.

With all equal sides and equal angles, it has to be a square. What are the categories of quadrilaterals that include a square?

To classify the quadrilateral formed by Tony's wire, we need to consider its properties, specifically the lengths of its sides and the measures of its angles.

(Part A)

Since the wire was bent into a quadrilateral with sides of equal length and angles of equal measure, there are a few possible names that could fit:

1. Square: A square is a quadrilateral with all four sides of equal length and all four angles of equal measure (right angles of 90 degrees). If all the angles are right angles, then the quadrilateral would be a square.

2. Rectangle: A rectangle is a quadrilateral with all four angles equal to 90 degrees, but it does not require all four sides to be equal in length. So if the angles are right angles, but the sides are not necessarily equal in length, then it would be a rectangle.

3. Rhombus: A rhombus is a quadrilateral with all four sides of equal length, but opposite interior angles may not be equal like in a square. Therefore, if the sides are equal in length but not necessarily right angles, then it would be a rhombus.

4. Parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel. It does not require all sides to be equal like a square or rectangle, nor does it require any specific angle measures. If all sides are equal in length, then the parallelogram would also be a rhombus.

So, the possible names that fit the description are square, rectangle, rhombus, and parallelogram.

(Part B)

To justify the answer with evidence, we can use the properties of the quadrilaterals mentioned earlier.

For a square to be formed, it is necessary that all angles measure 90 degrees (right angles). So, if Tony's quadrilateral has right angles at each vertex, then it would be a square.

For a rectangle, all angles need to be right angles as well, but the sides do not have to be equal. Thus, if Tony's quadrilateral has right angles at all vertices and sides that are not necessarily equal, then it would be a rectangle.

If the sides of Tony's quadrilateral are equal in length but the angles are not necessarily right angles, it would be a rhombus.

Finally, if Tony's quadrilateral has opposite sides that are parallel, it would be a parallelogram. And if the sides are equal in length as well, then it would also be a rhombus.

To determine the exact classification of the quadrilateral, it would be helpful to measure the angles or provide more specific information about the sides and angles.