Kathleen says that all quadrilaterals have right angles. Grace says that quadrilaterals do not have to have right angles. Explain who is correct. A. Kathleen is correct because rectangles have four right angles. B. Grace is correct because quadrilaterals have no right angles. C. Kathleen is correct because quadrilaterals have four equal angles. D. Grace is correct because a rhombus may not have right angles.
The Correct Answer and Explanation is:
Correct Answer: D. Grace is correct because a rhombus may not have right angles.
Explanation:
The definition of a quadrilateral is a polygon with four sides. This is a very broad category that includes many different shapes, such as squares, rectangles, parallelograms, rhombuses, trapezoids, and irregular four-sided figures.
Kathleen claims that all quadrilaterals have right angles. This statement is incorrect. While it is true that some quadrilaterals like rectangles and squares have right angles, this is not true for every quadrilateral. For example, a trapezoid usually has only one pair of parallel sides and may have no right angles at all. Similarly, a rhombus is a quadrilateral with all four sides equal in length, but it does not necessarily have right angles. The angles in a rhombus can be acute or obtuse, depending on its shape.
Grace, on the other hand, says that quadrilaterals do not have to have right angles. This is accurate. A quadrilateral only needs to have four sides. The presence or absence of right angles depends on the specific type of quadrilateral. Therefore, Grace’s statement reflects a broader and more accurate understanding of the category.
Option D best supports Grace’s position by providing a correct example: a rhombus may not have right angles, which proves that right angles are not required in all quadrilaterals.
Option A is misleading because it refers only to rectangles, which are a specific type of quadrilateral, not a general rule. Option B is false because some quadrilaterals do have right angles. Option C is incorrect because not all quadrilaterals have equal angles.
In conclusion, Grace is correct because quadrilaterals vary in shape, and right angles are not a requirement for all of them.
