Is this quadrilateral a rhombus?
Let’s begin by recalling the definition of a rhombus. A rhombus is a quadrilateral with four sides of equal lengths. We can see in the diagram that blue lines have been added to the four sides of the rhombus. These lines indicate that they are all the same length. Therefore, the condition required for this quadrilateral to be a rhombus is fulfilled. And so our answer to the problem is yes.
Now, you may be wondering, could this quadrilateral be a square? And the answer is yes, it still could be. A square also has four sides of equal length. So square is an example of a rhombus.
However, squares also have a special property that not all rhombuses share: their four interior angles are all right angles. So square is in fact just a special type of rhombus.
We haven’t been given any information about the angles in this quadrilateral. So we don’t know whether or not it’s also a square. In any case, whether this quadrilateral is a square or not, it’s still a rhombus. And so our answer to the problem is yes.