∴ 180 -∠3=∠DBA, 180 -∠4=∠CBA
∴∠DBA=∠CBA
In △ ADB and △ACB,
∠ 1=∠2 (known)
AB=AB (male side)
∠DBA=∠CBA (certification)
∴△ADB≌△ACB(ASA)
∴AC=AD (the corresponding sides of congruent triangles are equal)
Prove that the distance from ∵C to A and D is equal.
∴AC=BC
In delta △ACD and delta △CEB
AC=BC (certification)
∠CEB=∠CDA (known)
∠C=∠C (angle * * *)
∴△ACD≌△CEB
∴AD=BE (the corresponding sides of congruent triangles are equal)
(1) Prove that the advertisement of (6) is high.
∴∠ADC=∠ADB=90
In RT△ADC and RT△ADB.
AD=AD (male side)
AB=AC (known)
∴△ADC≌ADB(HL)
∴BD=CD (the corresponding sides of congruent triangles are equal)
(2) Proof: ∫△ADC≌ADB (proven)
∴∠BAD=∠CAD
⒏ It is proved that ∵AC⊥CB,AB⊥DC.
∴∠C=∠B=90
In ACB and DBC.
AB=DC (known)
CB=CB (male * * * side)
∴RT△ACB≌RT△DBC(HL)
∴∠ABD=∠ACD (the angles corresponding to congruent triangles are equal).
⒑ in Delta△ △AOB and Delta△ △DOC
OA=OC (known)
OB=OD (known)
∠AOB=∠DOC (equal to the vertex angle)
∴△AOB≌△DOC(SAS)
∴∠DCO=∠BAO (the corresponding angles of congruent triangles are equal).
∴DC∥AB (parallel method)
⒒∵ B, F, C, E are in a straight line, ab∨de, AC∨df.
∴∠ABC=∠DEF,∠ACB=∠DFE
∠ACB=∠DFE
∴FB﹢FC=BC,CE﹢FC=EF
∴BC=EF
In delta △DFE and delta △ACB
∠ABC=∠DEF (authentication)
∠ACB=∠DFE (certification)
BC=EF (certification)
∴△DFE≌△ACB(ASA)
∴AB=DE,AC=DF (the corresponding sides of congruent triangles are equal).