(1) Because AD∥BC, so ∠ADF=∠DEC. Because ∠ AFE = 180-∠ AFD, ∠ B =180-∠.
So it can be proved by ∠ADF=∠DEC, ∠AFD=∠DCE, △ADF∽△DEC (the angles of two triangles are the same, so the two triangles are similar. )
(2) Because △ADF∽△DEC, AF/DC=AD/DE. Because AB=DC, AF/AB=AD/DE. Substitute the above values for calculation and get DE= 12. △ADE is a right triangle because AE⊥BC and AE⊥AD. Damn it, AE =DE？ -Advertising? = 144- 108=36，AE=6。
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