in the figure below, points d, e, and f are the midpoints of the sides of abc. suppose ac =72 df = 34 and ab =48. find the following lengths

Applying the triangle midsegment theorem, the following lengths are calculated as:
BC = 68
DE = 36
CE = 34
Given:
AC = 72
DF = 34
AB = 48
Find BC:
BC = 2(DF)
BC = 2(34)
BC = 68
Find DE:
DE = 1/2(AC)
DE = 1/2(72)
DE = 36
Find CE:
CE = 1/2(BC)
CE = 1/2(68)
CE = 34
Thus, applying the triangle midsegment theorem, the following lengths are calculated as:
BC = 68
DE = 36
CE = 34
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