7. 如图,$E$ 为线段 $BC$ 上一点,$AB ⊥ BC$,$△ ABE ≌ △ ECD$, 判断 $AE$ 与 $DE$ 的关系, 并证明你的结论.

7.解:$AE=DE,AE ⊥ DE.$
证明:$\because AB ⊥ BC, \therefore ∠ B=90°, \therefore ∠ A+∠ AEB=90°.$
$\because △ ABE ≌ △ ECD, \therefore AE=DE, ∠ A=∠ DEC,$
$\therefore ∠ DEC+∠ AEB=90°, \therefore ∠ AED=90°, 即 AE ⊥ DE.$

8. 如图,$△ ABD ≌ △ CFD, AD ⊥ BC$于点$D$.
(1)求证:$CE ⊥ AB$;
(2)若$BC=7,AD=5$,求$AF$的长.

8.(1)证明:$\because △ ABD ≌ △ CFD, \therefore ∠ BAD=∠ FCD.$
又$\because ∠ AFE=∠ CFD, \therefore ∠ AEF=∠ CDF=90°,$
$\therefore CE ⊥ AB.$
(2)解:$\because △ ABD ≌ △ CFD, \therefore BD=DF.$
$\because BC=7,AD=DC=5, \therefore BD=BC-CD=2,$
$\therefore AF=AD-DF=5-2=3.$

9. 如图,A,D,E 三点在同一条直线上,且$△ BAD ≌ △ ACE$.
(1)求证:$BD=DE+CE$;
(2)当$△ ABD$满足什么条件时,$BD // CE$?

9.(1)证明:$\because △ BAD ≌ △ ACE, \therefore BD=AE,AD=CE.$
$\because AE=DE+AD, \therefore BD=DE+CE.$
(2)解:当$∠ ADB=90°$时,$∠ BDE=90°=∠ E,$
$\therefore BD // CE.$