1) Isosceles [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{DE} \perp \overline{AC}[/tex], [tex]\overline{DF} \perp \overline{BC}[/tex], [tex]\overline{DE} \cong \overline{DF}[/tex] (given)
2) [tex]\angle CAB \cong \angle CBA[/tex] (angles opposite congruent sides in a triangle are congruent)
3) [tex]\angle AED[/tex] and [tex]\angle DFB[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\angle AED \cong \angle DFB[/tex] (all right angles are congruent)
5) [tex]\triangle DEA \cong \triangle DFB[/tex] (AAS)
6) [tex]D[/tex] is the midpoint of [tex]\overline{AB}[/tex] (if a point splits a segment into two congruent parts, it is a midpoint)
