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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 \(\overline{DE}\) 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 12, 2021
 #1
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I count 7 isosceles triangles.

 Feb 12, 2021

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