(I)∵△ABC中,D、E分别为AB、AC中点,∴DE∥BC
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/a2cc7cd98d1001e98b01e7bebb0e7bec54e79746?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
∵DE?面PBC且BC?面PBC,∴DE∥面PBC;
(II)连结PD
∵PA=PB,D为AB中点,∴PD⊥AB
∵DE∥BC,BC⊥AB,∴DE⊥AB,
又∵PD、DE是平面PDE内的相交直线,∴AB⊥平面PDE
∵PE?平面PDE,∴AB⊥PE;
(III)∵PD⊥AB,平面PAB⊥平面ABC,平面PAB∩平面ABC=AB
∴PD⊥平面ABC,可得PD是三棱锥P-BEC的高
又∵PD=
,S
△BEC=
S
△ABC=
∴三棱锥B-PEC的体积V=V
P-BEC=
S
△BEC×PD=