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 ${60}^o$ 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

Answer 1

The terms need to defined are:

i) Polygon is a closed figure bounded by three or more line segments.

ii) Line segment is a part of a line with two end points.

iii) Line undefined term.

iv) Point undefined term.

v) Angle in a figure is formed by two rays with one common initial point.

vi) Acute angle is an angle whose measure is between

$0°$ to $90°$.

Line and point are undefined terms.

All the angles are $60°$ each equilateral triangle and two line segments are equal to third one, therefore all three sides of an equilateral triangle are equal (according to Euclid's axiom, things which are equal to the same thing are equal to one another).