Given some angle [math]ABC[/math],[br][list][br][*] Create point [math]D[/math] on either line segment [math]\overline{BA}[/math] or [math]\overline{BC}[/math][br][br][/*][*] Using the [b]Compass tool[/b], construct a circle with radius [math]m\overline{BD}[/math] centered @ point [math]B[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the point of intersection ([math]E[/math]) between your circle and the segment not containing point [math]D[/math][br][br][/*][*] Create point [math]F[/math], not on angle [math]\angle{ABC}[/math][br][br][/*][*] Using the [b]Compass tool[/b], construct a circle with radius [math]m\overline{DF}[/math] centered @ point [math]D[/math][br][br][/*][*] Using the [b]Compass tool[/b], construct another circle with radius [math]m\overline{DF}[/math] centered @ point [math]E[/math][br][br][/*][*] Using the [b]Intersect tool[/b], create the points of intersection ([math]G[/math] and [math]H[/math]) between the two most recently constructed circles ([math]d[/math] and [math]e[/math])[br][br][/*][*] Using the [b]Ray tool[/b], construct [math]\overrightarrow{BG}[/math][br][/*][/list]

[math]\overrightarrow{BG}[/math] is the angle bisector of [math]\angle{ABC}[/math].[br][br]What is the relationship between [math]\angle{ABG}[/math] and [math]\angle{GBC}[/math]? Use the [b]Angle tool[/b] to verify your answer.[br][br][br]Does your construction pass the Drag Test?