Creation of this resource was inspired by a comment from [url=https://twitter.com/MarchtoCharm]Bryan Johnson[/url] in response to [url=https://twitter.com/dynamic_math/status/1184831433241579520?s=20]this tweet[/url] originally inspired by [url=https://twitter.com/gogeometry]Antonio Gutierrez (GoGeometry)[/url]. See pic below. [br][br]Link to the original GeoGebra resource (special case of this illustration where 3 equilateral triangles are built off the sides of this shaded triangle can be found [url=https://www.geogebra.org/m/kmdgzmhx]here[/url]).

In the GeoGebra applet below, the triangles built off the sides of the shaded triangle are all similar to each other. [b][color=#ff00ff]You can control the size of one angle of these similar triangles by adjusting the slider in the middle[/color]. [/b] [br][br]The LARGE POINTS are MOVEABLE. [br][b][color=#1e84cc]The slider off to the left controls the size of the lower left angle within the shaded triangle.[/color] [br][br][color=#ff00ff]How can we formally prove what is dynamically illustrated here? [/color][/b]