The segments AB and DC lie on parallel lines, and the segments AC and BD intersect at point M. Find MC if AB = 12, DC = 48, AC = 35

bystudin | May 31, 2020 | Education

Consider the triangles ABM and CDM.
∠AMB = ∠CMD (since they are vertical).
∠BAM = ∠MCD (since they are internal cross-lying).
Therefore, according to the first sign of the similarity of triangles, these triangles are similar.
Then, we can write:
DC / AB = MC / AM
48/12 = MC / AM
4 = MC / AM
4 = MC / AM
MC = 4AM
AC = AM + MC (as shown)
35 = AM + 4AM
35 = 5AM
AM = 7
MC = 4AM = 4 * 7 = 28
answer: MC = 28

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.