Chứng minh −−→ A C + −−→ B D = −−→ A D + −−→ B C .

Ta có \(\overrightarrow {AC} + \overrightarrow {BD} = \overrightarrow {AD} + \overrightarrow {DC} + \overrightarrow {BC} + \overrightarrow {CD} \)

\( = \left( {\overrightarrow {AD} + \overrightarrow {BC} } \right) + \left( {\overrightarrow {DC} + \overrightarrow {CD} } \right) = \left( {\overrightarrow {AD} + \overrightarrow {BC} } \right) + \overrightarrow {DD} = \overrightarrow {AD} + \overrightarrow {BC} \).