Question

Hello,
'An equilateral triangle is a polygon made uo of three line segments out of which two line segments are equal to the third one and all it's 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 angles are equal in an equilateral triangle!??
Plzz Answer!!♥

Answer 1

✔✅An equilateral triangle is a triangle whose three sides all have the same length. They are the only regular polygon with three sides, and appear in a variety of contexts, in both basic geometry and more advanced topics such as complex number geometry and geometric inequalities.
✔✅Because the equilateral triangle is, in some sense, the simplest polygon, many typically important properties are easily calculable. For instance, for an equilateral triangle with side length , we have the following:

✴The altitude, median, angle bisector, and perpendicular bisector for each side are all the same single line.

✴These 3 lines (one for each side) are also the lines of symmetry of the triangle.

✴All three of the lines mentioned above have the same length of .

✴The area of an equilateral triangle is .

✴The orthocenter, circumcenter, incenter, centroid and nine-point center are all the same point. The Euler line degenerates into a single point.

✴The circumradius of an equilateral triangle is . Note that this is the length of an altitude, because each altitude is also a median of the triangle.

✴The inradius of an equilateral triangle is . Note that the inradius is the length of an altitude, because each altitude is also a median of the triangle. Also the inradius is the length of a circumradius.
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