G.GCO.11 Angle Bisector Construction Action!

The applet below illustrates how we can use a compass and straightedge to[b] bisect any given angle. [/b][br][br][b][color=#0000ff]Can you formally prove why this method of construction is valid? [/color][/b][br](For a hint, [url=https://www.geogebra.org/m/fskReBGs]click here[/url].)
Quick (Silent) Demo: 0:00 to 1:00

Information: G.GCO.11 Angle Bisector Construction Action!