已知,如图,在RT△ABC与RT△A1B1C1中,∠A=∠A1,AD⊥BC,A1D1⊥B1C1,垂足分别为点D,D1,AB/A1B1=AD/A1D1,求证△ABC相似△A1B1C1
问题描述:
已知,如图,在RT△ABC与RT△A1B1C1中,∠A=∠A1,AD⊥BC,A1D1⊥B1C1,垂足分别为点D,D1,AB/A1B1=AD/A1D1,求证△ABC相似△A1B1C1
答
证明:
∵AD⊥BC,A1D1⊥B1C1
∴∠ADB=∠A1D1B1=90
∵AB/A1B1=AD/A1D1
∴RT△ABD∽RT△A1B1D1
∴∠B=∠B1
∵∠A=∠A1
∴△ABC∽△A1B1C1