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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?

 Feb 13, 2021
 #1
avatar+1028 
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There are 7 isosceles triangles:

1/  ABC

2/  ABD

3/  BCD

4/  BDE

5/  CDE

6/  DEF

7/  CEF

 Feb 13, 2021

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