如图,过▱ABCD的顶点A的直线交BD于点P,交CD于点Q,交BC的延长线于点R. 求证:PQ/PR=PD2PB2.

问题描述:

如图,过▱ABCD的顶点A的直线交BD于点P,交CD于点Q,交BC的延长线于点R.
求证:

PQ
PR
PD2
PB2

证明:∵四边形ABCD是平行四边形,
∴AD∥BC,AB∥CD,
∴△APD∽△RPB,△DPQ∽△BPA,

PA
PR
=
PD
PB
PQ
PA
=
PD
PB

∴两式相乘得:
PQ
PR
=
PD2
PB2