Question 14 Marks
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 a equilateral triangle.
Answer
View full question & answer→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^\circ $ to $90^\circ .$
Here undefined terms are line and point.
All the angles of equilateral triangle are $60^\circ $ 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.
$i.$ 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^\circ $ to $90^\circ .$
Here undefined terms are line and point.
All the angles of equilateral triangle are $60^\circ $ 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.