Is a rhombus a square? Yes or No? Why?
The correct answer and explanation is:
No, a rhombus is not necessarily a square.
A rhombus and a square are both types of quadrilaterals with four equal sides, but they differ in other key properties that distinguish them. The primary difference lies in the angles of the shapes.
A rhombus has all four sides of equal length, but its interior angles are not necessarily 90 degrees. The angles in a rhombus are opposite and equal, and the adjacent angles are supplementary, meaning they add up to 180 degrees. However, the angles are generally oblique (less than or greater than 90 degrees). A rhombus does not require the angles to be right angles.
A square, on the other hand, is a specific type of rhombus where all the properties of a rhombus hold, but it also has the additional requirement that all its angles must be right angles, each measuring exactly 90 degrees. This requirement is what makes a square a special type of rhombus.
Therefore, while every square is a rhombus because it satisfies the condition of having four equal sides, not every rhombus is a square because a rhombus can have angles that are not right angles. A rhombus only becomes a square if all of its angles are 90 degrees, which is the defining characteristic of a square.
In summary, a rhombus is a more general shape, and a square is a specialized case where the rhombus has right angles. The distinction comes down to the angle measurements—if the rhombus has right angles, it is a square, otherwise it remains a rhombus.