Question : ABCD is a quadrilateral in which AB || DC. E and F are the midpoints of the diagonals AC and BD, respectively. If AB = 18 cm and CD = 6 cm, then EF =?
Option 1: 8 cm
Option 2: 6 cm
Option 3: 12 cm
Option 4: 9 cm
Correct Answer: 6 cm
Solution :
In a trapezium, a line joining the mid-points of the diagonals is equal to half of the difference of two parallel sides.
So, EF = $\frac{1}{2}$ (AB – CD)
= $\frac{1}{2}$ (18 – 6)
= $\frac{1}{2}$ × 12
= 6
Hence, the correct answer is 6 cm.
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