Can the points A, B and C belong to the same line, if AB > BC, AB > AC, and AB < AB + BC?
1
Expert's answer
2010-06-14T06:18:02-0400
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:
1) AB = BC + AC 2) AC = AB + BC 3) BC = AB + AC
The first statement is not true because AB < AB + BC (it’s the given information). The second statement is not true because AB > AC, so AB + BC > AC too, thus AC is not equal to AB+BC. The third statement is not true because AB > BC, so AB + AC > BC too, thus BC is not equal to AB+AC. So we can conclude that the points A, B and C can not belong to the same line.
Numbers and figures are an essential part of our world, necessary for almost everything we do every day. As important…
APPROVED BY CLIENTS
"assignmentexpert.com" is professional group of people in Math subjects! They did assignments in very high level of mathematical modelling in the best quality. Thanks a lot
Comments
Leave a comment