7. 如图,过正方形ABCD的顶点D作DE//AC交BC的延长线于点E.
(1)判断四边形ACED的形状,并说明理由.
(2)若BD=8 cm,求线段BE的长.

7.(1)证明:$\because$四边形$ABCD$为平行四边形,
$\therefore AD// BC$,即$AD// CE$,
又$\because AC// DE$,
$\therefore$四边形$ACED$为平行四边形.
(2)$BE=8\sqrt{2}\ \mathrm{cm}$

8. 如图,在在正方形ABCD中,E为对角线AC上一点,连结EB,ED.
(1)求证:△BEC≌△DEC.
(2)延长BE交AD于点F,若∠DEB=140°,求∠AFE的度数.

8.(1)证明:$\because$四边形$ABCD$为正方形,
$\therefore CB=CD$,$∠ BCA=∠ DCA$,
$\because CE=CE$,$\therefore△ BEC≌△ DEC$.
(2)解:$\because△ BEC≌△ DEC$,
$\therefore∠ DEC=∠ BEC=\dfrac{1}{2}∠ DEB=70°$,
$\therefore∠ AEF=∠ BEC=70°$,
$\because AC$平分$∠ BAD$,$∠ BAD=90°$,
$\therefore∠ CAD=45°$,$\therefore∠ AFE=65°$.

9. 如图,将边长为2的正方形OABC如图放置,O为原点.若∠α=15°,则点B的坐标为.

9.$(-\sqrt{2},\sqrt{6})$