Question

已知梯形中，于于

相交于的中點(diǎn)

(1)若點(diǎn)為線段上一點(diǎn)，且過點(diǎn)作于試證：

(2)求證：

 

Answer 1

(1)∵為中點(diǎn)，

      ∴

      又∵且

      ∴

      ∴在和中，

      ∴ ······································3分

      ∴

      又∵

      ∴

      即：··········································4分

    又∵

     ∴

連接

∵

∴為的角平分線

  ∵

∴ ·················································5分

(2)過作交的延長線于

      ∵梯形中，  

∴

      又∵

      ∴四邊形為， 

∴ ·················6分

      ∵ 又且

      ∴

      ∴為等腰直角三角形

      又∵ ∴

      ∴

      ∴ ·············································7分

      ∵

      ∴

      ∵

      ∴在和中

      ∴ ···············································9分

      ∴

      ∵

    ∴···············································10分

 

解析:略