Question

If a figure is a square then it is a regular quadrilateral is this true or false?

Answer 1

Hint: One object is the same as another object if they possess the same properties. A square is a polygon with four equal sides and each angle should be ${90^ \circ }$ . Now what to do is discuss properties of quadrilaterals and check whether squares satisfy all these properties or not.

Complete step-by-step answer:

A square is a four sided polygon whose all four sides are the same and all four angles made by adjacent sides are equal to ${90^ \circ }$ .
Now from the diagram, let there be a square $ABCD$ with four sides namely $AB,BC,CD$ and $DA$ with diagonal $d$ and angles $\angle ABC,\angle BCD,\angle CDA,\angle DAC$ .
Now, we have to prove that the square is quadrilateral.
What we will do is we will check whether the square satisfies all minimum required properties to be quadrilateral.
Now, what quadrilateral is, it is a polygon with four sides and four vertices. Quadrilaterals can take any shape but the only condition is that the polygon must have sides and four vertices.
Now, from the figure we can see that the square $ABCD$ has four sides namely $AB,BC,CD$ and $DA$ and four vertices namely $A,B,C$ and $D$ . Hence , the square is quadrilateral.

Note: for this type of questions Students must be kept in mind about the properties of square, parallelogram, quadrilateral etc. We need to satisfy only those conditions of quadrilateral which are minimum required.