A straight line? Without being given any more information, can I conclude...?

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Hey guys,I just thought of a question which I thought was obvious but my text book has me a bit confused.

Say I have a stright line --------------------------
A D E B

Without being given anything information,can I conclude
AD+EB=AB/addition postulate
de=de reflexive
thus ad+de=be+de
ae=bd?
 
Hey guys,I just thought of a question which I thought was obvious but my text book has me a bit confused.

Say I have a stright line --------------------------
A D E B

Without being given anything information,can I conclude
AD+EB=AB/addition postulate
de=de reflexive
thus ad+de=be+de
ae=bd?
If, by AD+EB you mean the line of the length of segment AD plus the length of segment DE, then the answer to your "can I conclude AD+EB=AB" is no, unless the length of segment DE is zero. If that is not what you mean, then just what do you mean by the statement?
 
If, by AD+EB you mean the line of the length of segment AD plus the length of segment DE, then the answer to your "can I conclude AD+EB=AB" is no, unless the length of segment DE is zero. If that is not what you mean, then just what do you mean by the statement?

thank you again,you have answered my question,your right if I'm not given anything I wouldn't really know the length to conclude anything.
 
Say I have a stright line --------------------------
A D E B

Without being given anything information,can I conclude
AD+EB=AB/addition postulate

Well, not quite. You're close though. What you have is basically saying: Measure the distance from point A to point D, then measure the distance from point E to point B. Add those two together and you'll get the distance from point A to point B. But, if we use actual numbers, we'll see that can't be right.

Say the line segment AB has length 14. Divide it up into two other segments, as you've shown. Let's say that the line segment AD has length 5. And the line segment EB has length 6. According to your formula, the distance of line segment AB would be 11, which we know isn't true. In fact, we're missing the length of the line segment DE, which in this case we know has to be 3.

de=de reflexive
thus ad+de=be+de
ae=bd?

This part doesn't follow from the above. You can, of course, conclude that the length of line segment DE equals the length of line segment DE. However, the remaining two statements are only true under certain circumstances, not for every line. You can tell by looking at the above example using numbers. There, AE = AD + DE; AE = 5 + 3 = 8. And DB = DE + EB; DB = 3 + 6 = 9
 
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