ABCD is a quadrilateral in which AB ∥ DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 21 cm, BC = 33 cm, DC = 11 cm, and AD = 52 cm, then what is the length (in cm) of EF?
5
Since AB ∥ DC, the quadrilateral ABCD is a trapezium with AB and DC as its two parallel sides.
There is a standard result: in a trapezium, the segment joining the mid-points of the two diagonals is parallel to the parallel sides, and its length equals half the difference of the parallel sides.
That is, \(EF = \dfrac{|AB - DC|}{2}\).
Substitute the values: \(EF = \dfrac{|21 - 11|}{2} = \dfrac{10}{2} = 5\) cm.
Hence, the length of EF is 5 cm.
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