(本题6分)如图,四边形$ABGH$,四边形$BCFG$,四边形$CDEF$都是正方形,请从图中找出三对相似三角形,要求其中一对必须不是直角三角形,并说明这一对三角形相似的理由.<ImageHere>
解:$triangleABHsimtriangleGBH,triangleACHsimtriangleHFC,triangleBCHsimtriangleBHD$.其中$triangleBCHsimtriangleBHD$的理由如下:设小正方形的边长为1,则$BC=1,BH=sqrt{2},BD=2$.$thereforefrac{BH}{BC}=sqrt{2},frac{BD}{BH}=frac{2}{sqrt{2}}=sqrt{2}$.$thereforefrac{BH}{BC}=frac{BD}{BH}$.$becauseangleHBC=angleDBH$,$thereforetriangleBCHsimtriangleBHD$.