Let's recall the definitions of a rhombus and a square.
Always
Practice makes perfect
We want to state whether the square is always, sometimes, or never a rhombus. To do this, we will compare the definitions of these shapes.
Type of Quadrilateral
Definition
Rhombus
A rhombus is a parallelogram with four congruent sides.
Square
A square is a parallelogram with four congruent sides and four right angles.
Looking at both definitions, we can see that the definition of a square contains the definition of a rhombus. Therefore, a square is always a rhombus. Note, however, that a rhombus is not necessarily a square!
Extra
Relationships Among Parallelograms
We know that a square is always a rhombus. To describe relationships between these types of parallelograms, we will also consider rectangles. Let's recall the definition of a rectangle.
Rectangle
A rectangle is a parallelogram with four right angles.
Knowing this definition, we can see that a square is a rectangle with four congruent sides. This means a square is also always a rectangle! Therefore, a square is a parallelogram that is both rectangle and rhombus. The Venn diagram summarizes the relationships between these parallelograms.
