An equilateral triangle is a triangle with three equal sides and three equal angles. Each angle in an equilateral triangle is equal to 60º, since the sum of the angles of a triangle is equal to 180º
Let the three angles of the equilateral triangle be X, Y and Z.
X + Y + Z = 180º (Sum of angles of a triangle)
Since the three angles of an equilateral triangle are equal, X = Y = Z. Hence Y and Z can be substituted by X.
X + X + X = 180º
3X = 180º
Examples of equilateral triangles are I Ching trigrams and the intersecting triangles in the star of David.
The star of David is I Ching or Yi Jing hexagram comprised of two intersecting equilateral triangles known as trigrams.
Since the sum of angles of a triangle is equal to 180º, the sum of angles of the two equilateral triangles in the star of David is equal to 360º.
Star of David = 2 Equilateral Triangles
= 2 x 180º
= 360º (angle at a point,)
Each side of the equilateral triangle is directly proportional to the opposite angle (equal to 60º), such that the three sides are in ratio 60:60:60.
Let the three sides be x, y and z. Therefore, x:y:z = 60:60:60. Dividing through by 60, the ratio is equal to 1:1:1.