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ABCDE is a pentagon prove that ab +bc +cd + de + ea =0
(AB+BC)+(CD+DE)+EA =AC+(CE+EA) =AC+CA both are equal in magnitude but opposite in direction thus, AC+CA=0
AB+BC+CD+DE+EA=(AB+BC)+CD+DE+EA=AC+CD+DE+EA=(AC+CD)+DE+EA=AD+(DE+EA)=AD+DA {ALL SOLUTIONS AND ADDITIONS ARE BASED ON THE TRIANGLE LAW OF VECTOR ADDITION} Now,both AD and DA are equal in magnitude but opposite in direction.i.e.AD+DA=0
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