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(1)菱形MNPQ.
连接AD、CE.
∵等边三角形
∴AB=CB BD=BE ∠ABC=∠DBE∴∠ABD=∠CBE∴△ABD≌△CBE∴AD=CE∵AQ=CQ DP=CP∴PQ=1/2AD,同理 PN=1/2CE NM=1/2AD MQ=1/2CE∴PQ=PN=NM=MQ∴四边形MNPQ是菱形
(2)成立.
连接AD、CE.
∵∠ABC=∠DBE∴∠ABD=∠CBE
∵AB=CB BD=BE ∴△ABD≌△CBE∴AD=CE∵AQ=CQ DP=CP∴PQ=1/2AD,同理 PN=1/2CE NM=1/2AD MQ=1/2CE∴PQ=PN=NM=MQ∴四边形MNPQ是菱形