Question

Read the following statement:
"A square is a polygon made up of four line segments, out of which, length of three line segments are equal to the length of fourth one and all its angles are right angles".
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all angles and sides of a square are equal?

Answer 1

The terms need to be defined are:
Polygon: A simple closed figure made up of three or more line segments.
Line segment: Part of a line with two end points.
Line: Undefined term.
Point: Undefined term.
Angle: A figure formed by two rays with a common initial point.
Ray: Part of a line with one end point.
Right angle: Angle whose measure is ${90}^o$.
Undefined terms used are: Line, Point.
Euclid's fourth postulate says that "all right angles are equal to one another".
In a square, all angles are right angles, therefore, all angles are equal (From Euclid's fourth postulate). Three line segments are equal to fourth line segment (Given).
Therefore, all the four sides of a square are equal. (by Euclid's first axiom "thing which are equal to the same thing are equal to one another.")