Read the following statement:
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 $$60^0$$ 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 term 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.
Acute angle: Angle whose measure is between $$0^0$$ and $$90^0$$.
Undefined terms used are: Line, Point Justification:
Two line segments are equal to third line segment
Therefore, all three sides of an equilateral triangle are equal All its angle are $$60^0$$ each. Therefore, all angles are equal (by Euclid's first axiom, things which are equal to same things are equal to one another.)
Hence, we can say that all sides and all angles are equal in an equilateral triangle.