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ABCDE is a pentagon prove that ab +bc +cd + de + ea =0

ABCDE is a pentagon prove that ab +bc +cd + de + ea =0

Grade:12

2 Answers

Arun
25757 Points
5 years ago
(AB+BC)+(CD+DE)+EA 

=AC+(CE+EA) 
=AC+CA 
both are equal in magnitude but opposite in direction 
thus, AC+CA=0
NACHIKETA PANDA
15 Points
2 years ago
  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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