The segments AB and CD are parallel, and O is the middle point of AD…

Step 1. The equal parts.

1. $\angle OAB = \angle ODC$, alternate angles, because $AB$ is parallel to $CD$.
2. $\angle AOB = \angle DOC$, vertically opposite angles.
3. $AO = DO$, because $O$ is the middle point of $AD$.

Step 2. The rule. $\triangle AOB \cong \triangle DOC$ by AAS. So $OB = OC$ by CPCT.

Step 3. The number. $OC = OB = 7\ \text{cm}$, so $BC = OB + OC = 14\ \text{cm}$.