The segment AC and BD, intersecting at point O, are divided in half and AB = 12cm. How many centimeters are CD?

Consider triangles AOB and COD:

AO = CO (according to the condition, point O is the middle of the AC);
DO = BO (by condition, point O is the middle of BD);
The angles AOB and COD are vertical, which means they are equal.

Thus, triangles AOB and COD are equal according to the first sign of equality of triangles (along two sides and the angle between them), which means that these triangles have the corresponding elements, that is, side AB = CD.

Since, according to the condition of the problem, AB = 12 cm, then CD = 12 cm.

Answer: 12 cm.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.