2) [tex]\overline{AG} \cong \overline{GC}[/tex] (a segment bisector divides a segment into two congruent segments)
3) [tex]\overline{EG} \cong \overline{GF}[/tex] (a segment bisector divides a segment into two congruent segments)
4) [tex]\angle AGE \cong \angle FGC[/tex] (vertical angles are congruent)
5) [tex]\triangle AGE \cong \triangle CGF[/tex] (SAS)
6) [tex]\angle FCG \cong \angle GAE[/tex] (CPCTC)
7) [tex]\overline{AE} \parallel \overline{FC}[/tex] (converse of alternate interior angles theorem)
8) [tex]\overline{AB} \parallel \overline{CD}[/tex] (segments collinear with parallel segments are parallel)
9) [tex]\angle DAC \cong \angle ACB[/tex] (alternate interior angles theorem)
10) [tex]\angle DAB \cong \angle DCB[/tex] (congruent angles added to congruent angles form congruent angles)
11) [tex]ABCD[/tex] is a parallelogram (a quadrilateral with two pairs of opposite congruent angles in a parallelogram)
