Question

Is a rhombus a square?

Answer 1

A square: is a quadrilateral that has four equal sides and four equal angles
A rhombus is a quadrilateral that has four equal sides
So, a quadrilateral that is a square is always a rhombus, because a square has four equal sides
But the converse is not true in general, because the definition of rhombus doesn't involve angles equality. Hence the only rhombi that are squares ar the rhombi that satisfy also the condition on angles. Precisely they are all the squares
We can the affirm that the set of squares is a subset of the set of rhombi
An example of rhombus that its not a square is a rhombus $ABCD$ inwhich $AB=BC=CD=AD=1$
$\overline{A}=\overline{C}={45}^o$ and $\overline{B}=\overline{D}={135}^o$