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.
square: 4 equal sides, 4 right angles.
as special cases, it is also a
rectangle: 4 right angles, 4 sides
rhombus: 4 equal sides
parallelogram: two pairs of parallel sides
trapezoid (generally a trapezoid has only two parallel sides, but don't gotta)
Part A: The quadrilateral can be classified as a square or a rhombus.
Part B: To justify this answer, we can use the properties of quadrilaterals.
1. A square is a quadrilateral with four sides of equal length and four right angles. Since the given quadrilateral has sides of equal length and angles of equal measure, it satisfies the properties of a square.
2. A rhombus is a quadrilateral with four sides of equal length. Since the given quadrilateral has sides of equal length, it also satisfies the properties of a rhombus.
Therefore, based on the given information, both square and rhombus are suitable classifications for the quadrilateral.
To classify the quadrilateral formed by Tony's wire, we need to determine which types of quadrilaterals have equal side lengths and angles of equal measure.
There are several names that fit the given conditions:
1. Square: A square is a type of quadrilateral with all sides of equal length and all angles of equal measure (right angles, 90 degrees).
2. Rhombus: A rhombus is a quadrilateral with all sides of equal length, but the angles are not necessarily 90 degrees.
To justify our answer, we need to show evidence that Tony's quadrilateral has sides of equal length and angles of equal measure.
For equal sides:
1. Measure each side of the quadrilateral using a ruler or measuring tape. Ensure that all four sides have the same measurement. If they are all the same, this indicates that the sides are equal in length.
For equal angles:
1. Measure the interior angles of the quadrilateral using a protractor. Each angle should ideally have the same measure, demonstrating that the angles are equal.
By performing these measurements and confirming equal side lengths and equal angle measures, we can determine whether Tony's quadrilateral is a square or a rhombus.