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Class 9-10, JEE & NEET
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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
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.