Answer to Question #288 in Geometry for Dave

Question

Can the points A, B and C belong to the same line, if AB = 1,8m, AC = 1,3m, DC = 3m?

Answer 1

According to the second Euclid's axiom, one of the three points on a line locates between two others. According to the third Euclid's axiom the length of the segment is the sum of parts of length, on which it can be broken by any of its points. So, if A, B and C belongs to the same line, one of the statements must be true:

AB = BC + AC
AC = AB + BC
BC = AB + AC

Substitute the given values:

1,8 = 3 + 1,3
1,3 = 1,8 + 3
3 = 1,8 + 1,3

So we can see there are no true statements, thus the points A, B and C can not belong to the same line.