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In a pentagon ABCDE, show that bar"AB" + bar"AE" + bar"BC" + bar"DC" + bar"ED" = 2bar"AC" - Mathematics and Statistics

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Sum

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

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Solution

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

Concept: Representation of Vector
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