Question

In a pentagon ABCDE, show that `bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED" = 2bar"AC"`

Answer 1

LHS = `bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED"`

`= (bar"AB" + bar"BC") + (bar"AE" + bar"ED" + bar"DC")`

`= bar"AC" + bar"AC"`

`= 2bar"AC"` = RHS