Show that $\vec{BB_1}=\vec{AA_1}+\vec{CC_1}$ $DABC$ and $DA_1B_1C_1$ are parallelograms. Show that $$\vec{BB_1}=\vec{AA_1}+\color{red}{\vec{CC_1}}$$

I noted that $$\vec{BB_1}=\vec{BA}+\vec{AA_1}+\vec{A_1B_1}\\\vec{BB_1}=\vec{BC_1}+\vec{C_1B_1}=\vec{BC}+\color{red}{\vec{CC_1}}+\vec{C_1B_1}$$
but nothing else.

$\vec{BB_1}=\vec{BA}+\vec{AA_1}+\vec{A_1D}+\vec{DC}+\vec{CC_1}+\vec{C_1B_1}$
Then use that the following sums are zero and cancel each other (opposite vectors):
$\vec{BA}+\vec{DC}=0$
$\vec{A_1D}+\vec{C_1B_1}=0$
