Are all the squares rhombuses

Short answer: yes, they are. Long answer: the definition of a rhombus tells us that it is a quadrilateral (a polygon containing 4 sides) and so it has the following features:

• Its internal diagonals are perpendicular among themselves;

• All its sides are congruent among themselves (they have the same length);
• The opposite internal angles are congruent (they have equal measures);

• The adjacent internal angles are supplementary (their sum is 180º).

As a matter of fact, the square also fulfils all these requirements. Therefore, it is also considered to be a rhombus.

And, are all the rhombuses squares?

The contrary is not true. For a polygon to be considered a square, besides all the requirements announced before, it is also required to possess the following feature:

• The internal angles must be right angles (90ºdegrees).

In conclusion, it cannot be said that all the rhombuses are squares, since not all the rhombuses possess this specific feature.

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