Explore the entire construction in the app above, then use the GeoGebra tools to draw segments [math]EG[/math] and [math]DG[/math], then consider the triangles [math]GEA[/math] and [math]GDA[/math].[br]Show that the two triangles are congruent, that proves that line [math]AG[/math] contains the bisector of the angle [math]BAC[/math].[br][br](Use the [i]Undo [/i]and [i]Redo [/i]buttons at the top right of the toolbar, or refresh the browser page to delete possible objects you have created but that are not useful or correct).

Define an angle bisector.

Two adjacent supplementary angles are such that one is three times the other, and their bisector form a [math]60°[/math] angle. Find the measure of each angle.

Two complementary angles are adjacent.[br]Find the measure of the angle created by their bisectors.

If a statement is false, correct it to make it true, or provide a counterexample.[br][br][list=1][*]The angle bisectors of vertical angles lay on the same line.[/*][*]Two complementary angles have the same line bisector.[/*][*]An angle can have more than one bisector.[br][/*][/list]