$證明????：(1)????由題意得????，CP=DQ，AM⊥MN，BN⊥MN，????$
$????CP⊥MN，DQ⊥MN????$
$在????△MPC????和????△NQD????中，$
$????\begin{cases}{CP=DQ }\\{∠MPC=∠NQD=90°}\\{MP=NQ} \end{cases}????$
$所以????△MPC≌△NQD(\mathrm {SAS})????$
$所以????∠ANM=∠BMN????$
$在????△ANM????和????△BMN????中$
$????\begin{cases}{∠ANM=∠BMN }\\{MN=MN}\\{∠AMN=∠BNM} \end{cases}????$
$所以????△ANM≌△BMN(\mathrm {ASA})????$
$所以????AM= BN????$
$????(2)????由題意得，????CP=DQ=1.6m ， AM=BN=9.6m ， PQ=12m????$
$因為????CP//BN，????$
$所以????△MPC∽△MNB????$
$所以????\frac {MP}{MN}=\frac {CP}{BN}????$
$因為????MP=xm，????????CP=1.6m，????????BN=9.6m????$
$所以????MN=6xm????$
$因為????PQ= MN-MP-NQ=12m????$
$所以????6x- x- x= 12????$
$解得，????x=3????$
$答:兩個路燈之間的距離????MN= 18m????$
$????(3)????設(shè)他在路燈????AM????下的影長是????ym????$
$由題意得????，\frac {y}{1.6}=\frac {18+y}{9.6}????$
$解得????，y=3.6????$
$答:他在路燈????AM????下的影長是????3.6m???$
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