1.has remained 2. slayed 3.felt 4 have paid5. arrives 6.hadnt seen 7 be heard8 will be covered 9. was working 10.suitsllhad expected 12 have been saved 13 were moved14is being widened 15 will become 16 is doing17 had been taught 18 has been regarded19 is spending 20 is allowed

19.(1)证明:∵AB=BD=AD=2√3,∴∠ADB=60°,又BC=CD=2,由余弦定理可得cos∠BCD+2-(2√3)12×2×22∴∠BCD=120°,即∠BDC=30°,∴∠ADC=90°,即CD⊥AD,而平面PAD⊥平面ABCD,∴CD⊥平面PAD,而PAC平面PAD,∴CD⊥PA.(2)解:设点O为AD的中点,连接PO、BO,由于△PAD、△ABD都为等边三角形,∴PO⊥AD、BO⊥AD,又平面PAD⊥平面ABCD,∴PO⊥平面ABCD,BO⊥平面PAD以AD,OB,OP所在的直线分别为x,y,z轴,建立如图所示的空间直角坐标系O-xyzO∵△PAD、△ABD都为等边三角形且边长为2√3,BC=CD=2,由(1)知AD⊥CDD(-√3,0,0),P(0,0,3),B(0,3,0),C(-3,2,0),∴P=(0,3,-3),D=(3,3,0=(-√3,2,-3),DC=(0,2,0)设平面PBD的一个法向量为n=(x,y,z)PB. n可得3x+3y=0令z=1,则y=1,x=-3,设平面PDC的一个法向量为m=(x,y,z)0由可得,3x+2y-3z=02于是y=0,令z=-1,则x=√∴m=(3,0,-1)n·m42√5cOS (n,n|·|m|255设二面角B-PD-C的大小为0,则cosb=2√5

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