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Introduction to Euclids Geometry — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsIntroduction to Euclids Geometry4 Marks
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.
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Answer

The terms need to be defined are:
  1. Polygon A closed figure bounded by three or more line segments.
  2. Line segment Part of a line with two end points.
  3. Line Undefined term.
  4. Point Undefined term.
  5. Angle A figure formed by two rays with one common initial point.
  6. 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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