What theorem(s) is/are dynamically illustrated below? [br](Feel free to move the white points or [color=#980000][b]brown point[/b][/color] anywhere you'd like!)
[color=#000000][b]Theorems:[/b][/color][br][br]If a triangle is equilateral, it is [color=#1e84cc][b]equiangular. [/b][/color][br][br]If [color=#980000][b]a point[/b][/color] lies on one side of an equilateral triangle and segments are drawn from [color=#980000][b]this point[/b][/color] to each of this equilateral triangle's 3 vertices, then these 3 segments can form another triangle whose [color=#1e84cc][b]largest angle [i]always measures 120 degrees. [/i][/b][/color]