Question

Prove
If |A-B|< (d/2) and |B-C|< (d/2) then |A-C| < d

Answer 1

A,B,C are 3 points right?

Answer 2

i mean i guess they could be.
Doesnt really specify. I'm just learning proofs in class right now so it doesn't technically state anything

Answer 3

i think A,B,C are 3 points, and |A - B| are distance between A and B and likewise for others
2 cases you can consider: first is all 3 points lie on a straight line...so distance A to B to C, you can draw a line and see that's obvious. second if they are not on straight line, they form a triangle, in a triangle the length of 2 side is always greater than the length of one side so:

|A - C| < |A - B| + |B - C| < d/2 + d/2 = d, therefore, |A - C| < d

Answer 4

i mean sum of length of 2 sides, ...forgot the sum in there