Medium
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 $60^{\circ}$ 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?
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 $60^{\circ}$ 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?
(N/A) The terms that need to be defined are:
$1$. Polygon: $A$ simple closed figure made up of three or more line segments.
$2$. Line segment: $A$ part of a line with two end points.
$3$. Angle: $A$ figure formed by two rays with a common initial point.
Undefined terms used in the definition are: Line,Point,Part.
Justification:
Given that two line segments are equal to the third one,by the property of transitivity,all three sides of the equilateral triangle are equal.
Since all angles are $60^{\circ}$ each,they are equal to one another. According to Euclid's first axiom,things which are equal to the same thing are equal to one another. Thus,all angles are equal.
$1$. Polygon: $A$ simple closed figure made up of three or more line segments.
$2$. Line segment: $A$ part of a line with two end points.
$3$. Angle: $A$ figure formed by two rays with a common initial point.
Undefined terms used in the definition are: Line,Point,Part.
Justification:
Given that two line segments are equal to the third one,by the property of transitivity,all three sides of the equilateral triangle are equal.
Since all angles are $60^{\circ}$ each,they are equal to one another. According to Euclid's first axiom,things which are equal to the same thing are equal to one another. Thus,all angles are equal.
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