bluecarneal wrote: An altitude of a pentagon is the perpendicular drop from a vertex to the opposite side. A median of a pentagon is the line joining a vertex to the midpoint of the opposite side. If the five altitudes and the five medians all have the same length, prove that the pentagon is regular. HI $\Delta ABD, DF \perp AB, AF=BF \Rightarrow DA=DB$ simmilary $\Delta EBC \equiv \Delta EBD \equiv \Delta ECA \equiv \Delta ADC \equiv \Delta ABD \Rightarrow AB=BC=CD=DE=EA \Rightarrow ABCDE $ Regular Pentagon I wish that i didnt miss any thing

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Yeah, a small comment: Quote: the five altitudes and the five medians all have the same length is meant as all altitudes have the same length, and all medians the same length, but the median could have a different length than an altitude, hence the key point is to prove that those 2 lengths are equal! At least this is what I understood! Best regards, sunken rock