如图,矩形ABCD,AB=2,AD=3,点P为AD上一点,PE⊥PC,交AB于E点,点Q在AP上不与P点重合,且QE⊥QC, (1)求证:AP•DP=AE•DC;(2)求AP+AQ的值.

问题描述:

如图,矩形ABCD,AB=2,AD=3,点P为AD上一点,PE⊥PC,交AB于E点,点Q在AP上不与P点重合,且QE⊥QC,

(1)求证:AP•DP=AE•DC;
(2)求AP+AQ的值.

(1)证明:∵四边形ABCD是矩形,∴AB∥CD,∠A=∠D=90°,∵PE⊥PC,∴∠EPC=90°,∴∠AEP+∠APE=90°,∠APE+∠DPC=90°,∴∠AEP=∠DPC,∵∠A=∠D,∴△AEP∽△DPC,∴APDC=AEDP,∴AP•DP=AE•DC.(2) 连接C...