+407 In triangle \(ABC, AB=AC, \angle ABC=72^{\circ},\) and segment \(\overline{BD}\) bisects \(\angle ABC\) with point D on side \(\overline{AC}.\) If point E is on side \(\overline{BC}\) such that segment \(\overline{DE}\) is parallel to side \(\overline{AB}\) ,and point F is on side \(\overline{AC}\) such that segment \(\overline{EF}\) is parallel to segment \(\overline{BD}\) ,how many isosceles triangles are in the figure shown?
