任意四边形连接对角线后分成了1,2,3,4,四个三角形,1跟3相对,2跟4...

如图,ABCD为任意四边形,对角线相交于O
S1=OA*ODsinα
S2=OA*OBsin(180-α)
S3=OB*OCsinα
S4=OC*ODsin(180-α)
S1*S3=OA*OB*OC*OD(sinα)^2    .(1)
S2*S4=OA*OB*OC*OD(sin(180-α))^2    .(2)
∵sinα=sin(180-α)
∴(1)=(2)
即S1*S3=S2*S4