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Geometry/Square, Rectangle, Rhombus, and Parallelogram

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Question
Hello sir

Sir Every square is also a rectangle, rhombus, and parallelogram
but how every sqaure is a rectangle because in sqaure all sides are equal and in rectangle opposite sides are equal and in parallaogram height is there but is square height is not there Then sir how we can say that every sqaure is rectangle and parallogram?

Answer
Hi Shilpa,

"Every square is also a rectangle, rhombus, and parallelogram."

That statement is true.  The converse of that statement is not true.  Be careful.

The definition of a square meets the requirements of the rectangle, rhombus, and parallelogram.  However, it does not work the other way around.  Most rectangles are not squares, clearly.  However, every square can be viewed as a rectangle where the sides just "happen" to be equal.  Every square can be viewed as a rhombus where the angles just happen to be right.  Every square can be viewed as a parallelogram where the sides happen to be equal and the angles happen to be right.

A square is the most specific of the quadrilaterals above.  Saying every square is also a rectangle is true.  But that does not mean every rectangle is a square.  Only some rectangles are squares.

I hope this has been helpful.

Regards,
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.

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