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 an 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 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°.
Here undefined terms are line and point.
All the angles of equilateral triangle are 60° each (given)
Two-line segments are equal to third one (given)
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.
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In the given figure, it is given that AC=BD,
Prove that AB=CD.
RS Aggarwal & V Aggarwal - Mathematics