作业帮几道关于全等三角形的题目
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/30 05:34:04
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?说出你的理由.
2、如图,长方形ABCD沿AE折叠,使点D落在BC边上的点F处,如果∠BAF=56°,则∠DAE与∠CEF为多少度?
3、如图,在△ABC中,AB=AC,AD是连接A与BC中点D的支架,AD和BC垂直吗?为什么?
4、如图,AB=AC,AD=AE,BD=CE,BD与CE相交于点O.
求证：∠CAB=∠EAD=∠BOC.
1、如图,△ABC中,∠ACB=90°,△ABC≌△DFC,你能判断DE与AB互相垂直吗?说出你的理由.
2、如图,长方形ABCD沿AE折叠,使点D落在BC边上的点F处,如果∠BAF=56°,则∠DAE与∠CEF为多少度?
3、如图,在△ABC中,AB=AC,AD是连接A与BC中点D的支架,AD和BC垂直吗?为什么?
4、如图,AB=AC,AD=AE,BD=CE,BD与CE相交于点O.
求证：∠CAB=∠EAD=∠BOC.
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
∠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