Read the following statements:
An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third-one and all its angles are
60° each.
Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles
are equal in a equilateral triangle.
The terms need to be defined are
(i) Polygon A closed figure bounded by three or more line segments.
(ii) Line segment Part of a line with two end points.
(iii) Line Undefined term.
(iv) Point Undefined term.
(v) Angle A figure formed by two rays with one common initial point.
(vi) Acute angle Angle whose measure is between 0° to 90°.
Here undefined terms are line and point.
All the angles of equilateral triangle are 60° each (given).
Two line segments are equal to the third-one (given).
Therefore, all three sides of an equilateral triangle are equal, because, according to Euclid’s axiom, things which are equal to the same thing are
equal to one another.
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