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Question
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° 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
- Polygon: A closed figure bounded by three or more line segments.
- Line segment: Part of a line with two endpoints.
- Line: Undefined term.
- Point: Undefined term.
- Angle: A figure formed by two rays with one common initial point.
- 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.
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