ABCDE is a pentagon, prove that

Question

Philoid · Accepted Answer

Given: ABCDE is a pentagon as shown below

Consider ΔABC and apply triangle law of vector, we get

Similarly, consider ΔADE and apply triangle law of vector, we get

And, consider ΔADC and apply triangle law of vector, we get

Adding (i), (ii) and (iii), we get

Add on both sides we get,

Or

Hence proved.