过点P作PM⊥AB于M,PN⊥CD于N,PG⊥BC于G
∵AB∥CD
∴∠ABC+∠DCB＝90
∵PM⊥AB,PG⊥BC,PM＝PG
∴BP平分∠ABC
∴∠CBP＝∠ABC/2
∵PN⊥CD,PG⊥BC,PN＝PG
∴CP平分∠DCB
∴∠BCP＝∠DCB/2
∴∠CBP+∠BCP＝（∠ABC+∠DCB）/2＝90
∴∠BPC＝180-（∠CBP+∠BCP）＝90°