Tính vế trái:

\(\overset{\rightarrow}{A B} + \overset{\rightarrow}{C D} + \overset{\rightarrow}{E A} = \left(\right. \overset{⃗}{B} - \overset{⃗}{A} \left.\right) + \left(\right. \overset{⃗}{D} - \overset{⃗}{C} \left.\right) + \left(\right. \overset{⃗}{A} - \overset{⃗}{E} \left.\right) = \overset{⃗}{B} + \overset{⃗}{D} - \overset{⃗}{C} - \overset{⃗}{E} .\)

Tính vế phải:

\(\overset{\rightarrow}{C B} + \overset{\rightarrow}{E D} = \left(\right. \overset{⃗}{B} - \overset{⃗}{C} \left.\right) + \left(\right. \overset{⃗}{D} - \overset{⃗}{E} \left.\right) = \overset{⃗}{B} + \overset{⃗}{D} - \overset{⃗}{C} - \overset{⃗}{E} .\)

Vậy hai vế bằng nhau, nghĩa là

\(\overset{\rightarrow}{A B} + \overset{\rightarrow}{C D} + \overset{\rightarrow}{E A} = \overset{\rightarrow}{C B} + \overset{\rightarrow}{E D} .\)

b,

Tương tự,

\(\overset{\rightarrow}{C D} + \overset{\rightarrow}{E A} = \left(\right. \overset{⃗}{D} - \overset{⃗}{C} \left.\right) + \left(\right. \overset{⃗}{A} - \overset{⃗}{E} \left.\right) = \overset{⃗}{A} + \overset{⃗}{D} - \overset{⃗}{C} - \overset{⃗}{E} ,\)

và

\(\overset{\rightarrow}{C A} + \overset{\rightarrow}{E D} = \left(\right. \overset{⃗}{A} - \overset{⃗}{C} \left.\right) + \left(\right. \overset{⃗}{D} - \overset{⃗}{E} \left.\right) = \overset{⃗}{A} + \overset{⃗}{D} - \overset{⃗}{C} - \overset{⃗}{E} .\)

Do đó

\(\overset{\rightarrow}{C D} + \overset{\rightarrow}{E A} = \overset{\rightarrow}{C A} + \overset{\rightarrow}{E D} .\)