Question

In figure D and E are point on the base BC of angle ABC such that BD equal to CE .prove that angle ABE congruent ANGLE ACD

Answer 1

Given :
BD   =  CE    and  AD   =   AE   and  

angle ADE   = angle AED ,


In ∆ ABE  and  ∆ ACD 

AE    =   AD                                          (  Given ) 

  angle ADE   =  angle AED                              (  Given )


And
BD  =  CE                                             ( Given )
We add both side DE and get 

BD  +   DE   =   CE  +   DE 

BE   =     DC  

Hence

angle  ABE =  angle ACD                         (  By SAS    rule   )                            ( Hence proved )

Answer 2

GIVEN :-
BD = CE and AD = AE and
angle ADE = angle AED
In ABE and ACD

AE = AD
(Given)
angle ADE = angle AED
(Given)


and
BD = CE
(Given)
we add both side DE and get
BD + DE = CE + DE
BE = DC
Hence
angle ABE = angle ACD
(By SAS rule)
(hence proved)





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