苏科版八年级上册数学补充习题答案2017

2017-03-28

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苏科版八年级上册数学补充习题答案2017(一)

探索三角形全等的条件(4)

1、∵ AB ∥ CD,

∴ ∠ABE = ∠CDF.

∵ AE ⊥ BD,CF ⊥ BD,

∴ ∠AEB = ∠CFD = 90°.

在△ABE和△CDF中,

∵ ∠ABE = ∠CDF,∠AEB = ∠CFD,

AE = CF,

∴ △ABE ≌ △CDF(AAS).∴ AB = CD.

2、∵ △ABC ≌ △DCB,

∴ AB = DC,∠A = ∠D.在△AOB和△DOC中,

∵ ∠A = ∠D,∠AOB = ∠DOC,AB = DC,

∴ △AOB ≌ △DOC(AAS).

3、(1) 在△ABE和△ACD中,

∵ ∠A = ∠A,∠B = ∠C,AE = AD,

∴△ABE ≌ △ACD(AAS).

(2)∵△ABE ≌ △ACD,

∴ AB = AC,AB - AD = AC - AE,即DB = EC.在△BOD和△COE中,

∵ ∠DOB = ∠EOC,∠B = ∠C, DB = EC,

∴ △BOD ≌ △COE(AAS).

苏科版八年级上册数学补充习题答案2017(二)

探索三角形全等的条件(5)

1、∵ B是EC的中点,

∴ BE = BC.

∵ ∠ABE = ∠DBC,

∴∠ABE + ∠ABD = ∠DBC + ∠ABD,

即∠DBE = ∠ABC.在△DEB和△ACB中,

∵ ∠DBE = ∠ABC,∠D = ∠A,

BE = BC,

∴ △DEB ≌ △ACB( AAS).

∴DE = AC.

2、∵ CD ⊥ AB,EF ⊥ AB,

∴ ∠CDB = ∠EFA = 90°,

∵ AD = BF,

∴ AD + DF = BF + DF,即AF = BD.在△CBD和△EAF中,

∵ CD = EF, ∠CDB = ∠EFA,BD = AF,

∴△CBD ≌ △EAF(SAS).

∴∠A = ∠B.

3、∵ ∠AFB = ∠AEC,∠B = ∠C,AB = AC,

∴ △ABF ≌ △ACE(AAS).

∴ ∠BAF = ∠CAE.

∴ ∠BAF - ∠EAF = ∠CAE - ∠EAF,即∠BAE = ∠CAF.

苏科版八年级上册数学补充习题答案2017(三)

探索三角形全等的条件(6)

1、连接BD.

∵ AB = CB, AD = CD,

BD = BD,

∴ △ABD ≌ △CBD(SSS).

∴ ∠A = ∠C.

2、∵AB = DC,AC = DB,BC = CB,

∴ △ABC ≌ △DCB(SSS).

∴ ∠ABC = ∠ DCB,∠ACB = ∠DBC.

∴ ∠ABC - ∠DBC = ∠DCB - ∠ACB,

即∠1 = ∠2.

3、△ABC ≌ △CDA( SSS),△ABE ≌ △CDF( SAS),

△ADF ≌ △CBE(SAS).证明略.

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