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Question:

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.

Solution:

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.