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# Geometry/Diagonals of Rectangles and Squares

Question
Hello sir

Sir i searched in internet  that Are there rectangles whose diagonals are perpendicular and equal in length? Yes, these are the special rectangles called squares - . Sir i have an confusion that if diagnals of recatangle are eqaul in lenght but lenght of rectangle are not equal in lenght , then how they can be called as sqaues.

Sir hope it is clear.

Hi Shilpa,

If the diagonals of a rectangle are equal and perpendicular, then the sides of the rectangle will be equal also, and the rectangle will indeed be a special rectangle: a square.

It is possible that the diagonals of the rectangle be equal and NOT perpendicular, in which case you will have a rectangle that is not a square.

So in short, if you have a rectangle AND the diagonals are equal, then it MUST be a square.
(If you would like an explanation as to why this is true, think about it for a bit, then ask a follow-up if you need.)

Hope this is clear,
Azeem

Geometry

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#### Azeem Hussain

##### Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

##### Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.