参考答案
1．A 2.C 3.C 4.C 5.C 6.150°
7．∵四边形ABCD是正方形，AC是对角线，∴∠ACD＝45°，∠BCD＝∠DCE＝90°.∴∠ACE＝135°.∵EC＝AC，∴∠E＝22.5°.∴∠AFC＝90°＋22.5°＝112.5°.
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8．D 9.D 10.AC＝BD或AB⊥BC 11.A 12.B 13.22.5 14.5－2 15. 2
DC＝BC，??
16．(1)证明：∵四边形ABCD是正方形，∴DC＝BC，∠B＝∠ADC＝90°.在△CDF和△CBE中，?∠CDF＝∠B＝90°，
??DF＝BE，∴△CDF≌△CBE.∴CF＝CE.
(2)∵△CDF≌△CBE，∴∠DCF＝∠BCE.∴∠ECF＝∠DCB＝90°.∵CF＝CE，∴∠CEF＝45°.
17．证明：(1)∵BD平分∠ABC，∴∠ABD＝∠CBD.又∵BA＝BC，BD＝BD，∴△ABD≌△CBD.∴∠ADB＝∠CDB.
(2)∵PM⊥AD，PN⊥CD，∴∠PMD＝∠PND＝90°.又∵∠ADC＝90°，∴四边形MPND是矩形．∵∠ADB＝∠CDB，PM⊥AD，PN⊥CD，∴PM＝PN.∴四边形MPND是正方形．
18．(1)证明：∵DE⊥BC，∴∠DFB＝90°.∵∠ACB＝90°，∴∠ACB＝∠DFB.∴AC∥DE.又∵MN∥AB，即CE∥AD，∴四边形ADEC是平行四边形．∴CE＝AD.
(2)四边形BECD是菱形．理由：∵D为AB中点，∴AD＝BD.又由(1)得CE＝AD，∴BD＝CE.又∵BD∥CE，∴四边形BECD是平行四边形．∵∠ACB＝90°，D为AB中点，∴CD＝BD.∴四边形BECD是菱形． (3)当∠A＝45°时，四边形BECD是正方形．理由：∵∠ACB＝90°，∠A＝45°，∴∠ABC＝∠A＝45°.∴AC＝BC.∵D为BA中点，∴CD⊥AB.∴∠CDB＝90°.∵四边形BECD是菱形，∴四边形BECD是正方形，即当∠A＝45°时，四边形BECD是正方形．
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