23.如圖1,在矩形ABCD中,AB=2,BC=5,BP=1,∠MPN=90°,將∠MPN繞點(diǎn)P從PB處開(kāi)始順時(shí)針?lè)较蛐D(zhuǎn),PM交邊AB于點(diǎn)E,PN交邊AD于點(diǎn)F,當(dāng)PE旋轉(zhuǎn)至PA處時(shí),∠MPN的旋轉(zhuǎn)隨即停止.
(1)如圖2,在旋轉(zhuǎn)中發(fā)現(xiàn)當(dāng)PM經(jīng)過(guò)點(diǎn)A時(shí),PN也經(jīng)過(guò)點(diǎn)D,求證:△ABP∽△PCD;
(2)如圖3,在旋轉(zhuǎn)過(guò)程中,
的值是否為定值?若是,請(qǐng)求出該定值;若不是,請(qǐng)說(shuō)明理由;
(3)設(shè)AE=m,連接EF,則在旋轉(zhuǎn)過(guò)程中,當(dāng)m為何值時(shí),△BPE與△PEF相似.