如图,在矩形ABCD中,E为BC中点,ED交AC于点P,DQ⊥AC于点Q,AB=kBC(1)当k=1时,CP/CE=?(2)当K=根号2时,求证AQ=QP
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![如图,在矩形ABCD中,E为BC中点,ED交AC于点P,DQ⊥AC于点Q,AB=kBC(1)当k=1时,CP/CE=?(2)当K=根号2时,求证AQ=QP](/uploads/image/z/11486299-67-9.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E7%9F%A9%E5%BD%A2ABCD%E4%B8%AD%2CE%E4%B8%BABC%E4%B8%AD%E7%82%B9%2CED%E4%BA%A4AC%E4%BA%8E%E7%82%B9P%2CDQ%E2%8A%A5AC%E4%BA%8E%E7%82%B9Q%2CAB%3DkBC%EF%BC%881%EF%BC%89%E5%BD%93k%3D1%E6%97%B6%2CCP%2FCE%3D%3F%EF%BC%882%EF%BC%89%E5%BD%93K%3D%E6%A0%B9%E5%8F%B72%E6%97%B6%2C%E6%B1%82%E8%AF%81AQ%3DQP)
如图,在矩形ABCD中,E为BC中点,ED交AC于点P,DQ⊥AC于点Q,AB=kBC(1)当k=1时,CP/CE=?(2)当K=根号2时,求证AQ=QP
如图,在矩形ABCD中,E为BC中点,ED交AC于点P,DQ⊥AC于点Q,AB=kBC
(1)当k=1时,CP/CE=?(2)当K=根号2时,求证AQ=QP
如图,在矩形ABCD中,E为BC中点,ED交AC于点P,DQ⊥AC于点Q,AB=kBC(1)当k=1时,CP/CE=?(2)当K=根号2时,求证AQ=QP
(1)∵AD∥CE,AD=BC=2CE
∴AP:PC=AD:CE
AP=2PC,CP=AC/3
∵正方形ABCD中,AC=√2BC=2√2CE
∴CP=2√2CE/3,CP/CE=2√2/3
(2)∵AD∥CE,AD=BC=2CE
∴DP:PE=AD:CE
DP=2PE,DP=DE·2/3
∵正方形ABCD中,AB=CD=√2BC=2√2CE,DE²=CD²+CE²
∴DE²=9CE²,DE=3CE
∴DP=DE·2/3=2CE=AD
在等腰三角形ADP中,DQ⊥AP
∴AQ=QP