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  • All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

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Answer: Rectangle or Square

Solution.
We know that sum of all angles of a quadrilateral is 360^{\circ}
If PQRS is a quadrilateral,
\angle P+\angle Q+\angle R+\angle S=360^{\circ}     …..(1)
It is given that all the angels are equal
i.e., \angle P=\angle Q=\angle R=\angle S
Put in equation 1 we get
4\angle P=360^{\circ}
\angle P=\frac{360^{\circ}}{4}
P = 90^{\circ}
Here all the angles of a quadrilateral are 90^{\circ}.
Hence given quadrilateral is either a rectangle or square. We cannot say which one it is, as nothing is given about the length of the sides.  

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