Answer:
EF = (d − b) / 2
Step-by-step explanation:
Let's say that G is the intersection of the trapezoid's diagonals.
Triangle GBC is similar to triangle GDA, so we can write a proportion:
GD / GB = AD / BC
GD / GB = d / b
GD = (d / b) GB
Next, F is the midpoint of BD, so BF equals FD.
BF = FD
GB + GF = GD − GF
2GF = GD − GB
2GF = (d / b) GB − GB
2GF = ((d − b) / b) GB
GF / GB = (d − b) / (2b)
Finally, triangle GBC is similar to triangle GFE, so we can write another proportion:
GF / GB = EF / BC
(d − b) / (2b) = EF / b
EF = (d − b) / 2
