In the given figure, AB parallel to PQ parallel to CD, AB= x units,CD=y units and PQ= z units, prove that 1/x+1/y=1/z
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see the diagram.
ΔABD and ΔPQD are similar, as the corresponding sides are parallel.
x / z = BD / QD => 1/x = QD /(z * BD)
ΔCDB and ΔPQB are similar, as corresponding sides are parallel.
y / z = BD / BQ => 1/y = BQ / (z * BD)
Add the two equations:
1/x + 1/y = (BQ + QD) / (z * BD) = 1 / z
ΔABD and ΔPQD are similar, as the corresponding sides are parallel.
x / z = BD / QD => 1/x = QD /(z * BD)
ΔCDB and ΔPQB are similar, as corresponding sides are parallel.
y / z = BD / BQ => 1/y = BQ / (z * BD)
Add the two equations:
1/x + 1/y = (BQ + QD) / (z * BD) = 1 / z
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