1.在△ABC中,AB=AC,過點(diǎn)C作射線CB′,使∠ACB′=∠ACB(點(diǎn)B′與點(diǎn)B在直線AC的異側(cè)),點(diǎn)D是射線CB′上一個(gè)動(dòng)點(diǎn)(不與點(diǎn)C重合),點(diǎn)E在線段BC上,且∠DAE+∠ACD=90°.
(1)如圖1,當(dāng)點(diǎn)E與點(diǎn)C重合時(shí),在圖中畫出線段AD.若BC=a,則CD的長(zhǎng)為
(用含a的式子表示);
(2)如圖2,當(dāng)點(diǎn)E與點(diǎn)C不重合時(shí),連接DE.
①求證:∠BAC=2∠DAE;
②用等式表示線段BE,CD,DE之間的數(shù)量關(guān)系,并證明.