Segments AB and CM intersect at point O so that AC || BM. Find the length of the segment CM, if AC = 15 cm, BM = 3 cm, CO = 10 cm.

univerkov | January 15, 2021 | education

Let us prove that triangles AOC and BOM are similar.
∠AOC = ∠BOM as vertical angles at the intersection of straight lines AB and CM
∠АСО = ∠ОМВ as criss-crossing angles at the intersection of parallel straight lines (by condition) АС and ВМ secant СМ. Then the triangles AOС and BOM are similar by the first sign of similarity of triangles, at two angles.
Then AC / BM = CO / CM.
15/3 = 10 / CM.
CM = 3 * 10/15 = 2 cm.
Answer: The length of the segment CM = 2 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.