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Geometry/Square, Rectangle, Rhombus, and Parallelogram

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Question
Hello sir

Sir if all geometric shapes like rombus , it is called as square and parallalogram, it is called as rectangle and in rectangle whose diagnals are equal , it is called as square. Then sir if they are same only then why all given different names and sir you told that diagonals are used to subdivide the diagonals then sir if they are same then why should we subdivide.,


I hope it is clear sir. Sir meaning of the question is like rombus it is called as square , parallalogram, it is called as rectangle, rectangle having same diagonals are called square, then , they are same then why should we subdivide them by using diagonals and giving different names and properies.What is the use of these in todays generation.

Answer
Hi Shilpa,

Rhombus, square, rectangle and parallelogram are all shapes that have different definitions.  However, some are special cases of others.  It is important to understand this principle of subsets.  All the above shapes are considered quadrilaterals.  But within the family of quadrilaterals, we have more specific shapes, such as a square.  So whenever we talk about squares, we are also talking about a specific type of quadrilateral.  This does not mean that every quadrilateral is a square or that all quadrilaterals are the same.  A square is a special case of a quadrilateral.
I am NOT saying "square=quadrilateral".  The statement only works ONE way.

A square is a quadrilateral.
A quadrilateral is--in general--NOT a square.
If the above is not clear, immediately ask a follow-up and request clarification.  The remainder of this response assumes you understand the above.

A quadrilateral is a polygon with 4 sides.
A parallelogram is a quadrilateral with two pairs of parallel sides.
A rhombus is a parallelogram with four equal sides.
A rectangle is a quadrilateral with four equal angles (i.e. right angles)
A square is quadrilateral with four equal sides and four equal angles.

Notice that there is some overlap in these definitions.  This describes which quadrilaterals are special cases of others.

Hope this helps,
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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