Q1.ABCD is a trapezium with AB || DC. E and F are points on non parallel sides AD and BC respectively such that EF || AB. Show that AE by ED = BF by FC.
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Explanation:
AB||DC and EF||AB
SO, EF∥DC
(because Lines that are parallel to same line are parallel to each other)
Join AC which intersects EF at M.
In △ADC ,
EM||DC (as EF||DC)
AE by ED = AM by MC
(Lines drawn parallel to one side of triangle intersects the other two sides in distinct points and divides the other two sides in same ratio.)
Similarly in △ABC , AB∥MF (as EF||AB)
SO,
AM by MC = BF by FC
AE by ED = AM by MC = BF by FC
Hence, AE by ED = BF by FC
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