from chapter circles
Asked by ridhisood | 22nd Feb, 2010, 06:58: PM
let ABCD be the trapezium such that AB II CD
we have to prove that
if AD=BC, then ABCD is cyclic.
construction:draw a line thru' C parallel to AD meeting AB in E.
then AECD is a parallelogram... as both pairs of opp sides are parallel.
angle ADC=angle AEC.....(i).. opp angles of a parallelogram
now, AD=BC.... given
AD=CE... opp sides of II gram
angle CEB=angle CBE
angle CEA+CEB=180... linear pair
so from (i) we get,
so quad ABCD is cyclic as one pair of opp angles is supplementary.
Answered by | 25th Feb, 2010, 04:43: PM
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