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As shown in the figure, in the known parallelogram ABCD, ab = 1 / 2ad, ab = AE = BF, explore the position relationship between EC and FD, and explain the reason
The relationship between EC and FD is: perpendicular to each other
It is proved that let the intersection of AD and EC be m, the intersection of BC and FD be n, connecting Mn
Because ABCD is a parallelogram,
So ad / / BC, AB / / DC, ab = DC,
Because AB = AE = BF,
So AE = BF = DC,
Because AB / / DC, AE = DC,
So am = DM = ad / 2,
Similarly: BN = CN = BC / 2,
So DM = CN,
So the quadrilateral amnb is a parallelogram,
So Mn = DC = AB,
Because AB = ad / 2, DM = ad / 2,
So Mn = DM,
So the parallelogram amnb is a diamond,
So EC and FD are perpendicular to each other
As shown in the figure, in the known parallelogram ABCD, ab = 1 / 2ad, ab = AE = BF, the position relationship between EC and FD is explored and explained
The relationship between EC and FD is: perpendicular to each other. It is proved that let the intersection of AD and EC be m, and the intersection of BC and FD be n, connecting Mn. Because ABCD is a parallelogram, so ad / / BC, AB / / DC, ab = DC, because AB = AE = BF, so AE = BF = DC, because
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