What definition(s) and theorems are dynamically illustrated below? [br](Feel free to move the [color=#ff00ff][b]pink vertices[/b][/color] anywhere you'd like!)
[color=#000000][b]Definition of an Equilateral Triangle:[/b][/color][br]A triangle is said to be an equilateral triangle if and only if it has at least 2 pairs of congruent sides. [br]More simply put, an equilateral triangle is a triangle that has 3 congruent sides. [br](Because an equilateral triangle has at least one pair of congruent sides, it is also an isosceles triangle.) [br][br]Thus, every theorem that applies to an isosceles triangle also holds true for an equilateral triangle. [br][b][color=#000000]These theorems are: [/color][/b][br][br]1) If two sides of a triangle are congruent, then the [color=#ff00ff][b]angles[/b][/color] opposite those sides are congruent. [br]2) The angle bisector of the [color=#1e84cc][b]vertex angle[/b][/color] of an isosceles triangle is the [b]perpendicular[/b] bisector of its base. [br][br][color=#000000][b]Other theorems[/b][/color] dynamically illustrated are as follows: [br][br]1) If a triangle is equilateral, then it is [color=#ff00ff][b]equiangular[/b][/color]. Each [color=#ff00ff][b]interior angle[/b][/color] measures [color=#ff00ff][b]60 degrees[/b][/color]. [br]2) A line of symmetry of an equilateral triangle splits it into 2 congruent [color=#ff7700][b]30-60-90 triangles[/b][/color].[br]3) In a [color=#ff7700][b]30-60-90 triangle[/b][/color], the hypotenuse is double the shorter leg.