Question

如图,AC⊥BC,BD⊥AD,AC=BD,AC、BD交于点O,求证:OC=OD

QQ的白纸图片上面涂鸦的三角形……

Answer 1

证明：∵△oac ∽△obd ∴oa/ob = oc/od
设 oc = x, od = y, ad = bc = k, 则
(y + k) y = (x+k)x
==> (x-y)(x+y+k)=0
==> x=y 即 oc = od

Answer 2

先证明全因为AC⊥BC,BD⊥AD，所以∠ADB=∠ACB=90° △ACB和△BDA为RT△
因为AC=BD，AB＝AB（公共边）所以RT△ACB≌RT△△BDA（HL）又因为AC、BD交于点O所以DO＝CO我蒙的你想抄就抄吧