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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

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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