Question

几道关于全等三角形的题目1、如图,△ABC中,∠ACB=90°,△ABC≌△DFC,你能判断DE与AB互相垂直吗?说出你

Answer 1

1、△ABC≌△DFC ∠AFE = ∠CFD = ∠B

∠ACB = 90° ∠A+∠B = 90°

∠AFE+∠A = 90°

∠AEF = 90°

即DE与AB垂直

2、△AEF≌△AED ∠EAF = ∠EAD = (90°-56°)/2 = 17°

∠D = 90° ∠AED = ∠AEF = 90°-17° = 79°

∠CEF = 180°-2*79° = 34°

3、AB = AC AD = AD BD = CD

△ABD≌△ACD ∠1 = ∠2 = 90°

即AD和BC垂直

4、AB = AC AD = AE BD = CE

△ABD≌△ACE

∠BAD = ∠CAE

∠BAD - ∠CAD = ∠CAE - ∠CAD

即∠CAB = ∠EAD

△ABD≌△ACE ∠B = ∠C

∠AFB = ∠CFO (对顶角相等)

∠CAB = ∠BOC

综上所述 ∠CAB=∠EAD=∠BOC