Marvin says that all rhombuses are squares. Aretha says that all squares are rhombuses. Who is correct? Explain.
The correct answer and explanation is:
The correct statement is Aretha’s: all squares are rhombuses. Marvin’s statement, that all rhombuses are squares, is false.
Explanation:
A rhombus is a type of quadrilateral with all four sides of equal length. However, its angles do not have to be right angles; they can be oblique. A square is a special type of rhombus because it has all four sides equal and all four angles equal to 90 degrees. Therefore, every square meets the criteria to be a rhombus, but with the additional property of right angles.
On the other hand, not all rhombuses are squares because many rhombuses have angles that are not right angles. For example, a diamond shape with four equal sides but angled corners is a rhombus but not a square.
To summarize, a square is a specific type of rhombus, meaning the set of all squares is a subset of the set of all rhombuses. This relationship is similar to how all squares are rectangles (because they have four right angles), but not all rectangles are squares (since rectangles do not require equal sides).
Therefore, Aretha’s statement “all squares are rhombuses” is true, while Marvin’s statement “all rhombuses are squares” is false. Understanding this helps clarify the hierarchy and classification of quadrilaterals in geometry.