Question

如图,在△CDE中,∠DCE=90°,CD=CE,DA⊥AB于A,EB⊥AB于B,试说明AB=AD+BE

Answer 1

你们教过全等吗?我用全等来证明.

∵∠A＝90∴∠ADC＋∠ACD＝90∵∠DCE＝90∴∠ADC＋∠BCE＝90∴∠ACD＝∠BCE

∵∠A＝∠B＝90,∠ACD＝∠BCE,DC=CE∴△ADC≌△BCE(AAS)∴AD=BC,AC=BE∵AB=AC+CB∴AB=AD+BE