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
答
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