如图,在△ABC与△A'B'C'中,AB=A'B',AC=A'C',AD,A'D'分别是两个三角形的高,且AD=A'D',试说明△ABC全等△A'B'C'

Question

如图,在△ABC与△A'B'C'中,AB=A'B',AC=A'C',AD,A'D'分别是两个三角形的高,且AD=A'D'
,试说明△ABC全等△A'B'C'

Answer 1

∵AD A'D'是高
∴∠ADB=∠ADC=∠A'D'B'=∠A'D'C'=90°
∵AD=A'D' AB=A'B'
∴△ABD≌△A'B'D'
∴BD=B'D'
同理CD=C'D'
∴BD+CD=B'D'+C'D'
即BC=B'C'
∵AB=A'B' AC=A'C'
∴△ABC≌△A'B'C