Are all the squares rectangles?

short answers for big questions

Short answer: According to the definition of rectangle, this polygon must comply with the following criteria cumulatively:

  • It must be a parallelogram (a convex quadrilateral which has two pairs of parallel sides);
  • All its internal angles are right angles (90º);
  • Its two diagonals are congruent (they have equal measures);
  • The opposite sides are congruent (they have equal measures).
The matter is that the squares also comply with all these requirements, and so it is also considered to be a rectangle.

square

And, are all the rectangles squares?

The contrary is not a reality. For a polygon to be considered a square, besides all the requirements mentioned before, it must also have the following features (having in mind that they are a consequence of each other):

  • Its internal diagonals are perpendicular among themselves;
  • All its sides are congruent among themselves (they have the same length);
Considering that not all the rectangles own these features, we cannot say that all the rectangles are squares.



escrever carta

Check out our List of Questions to get to know a little more about the most diverse topics related to mathematics. If you have any pertinent (math) question whose answer can not easily be found, send us an email on the Contact page with the question. We will be happy to respond. In the event that you detect any errors in our answers, do not hesitate to contact us!