SOLUTION: if c is the midpoint of aoverb and d lies on aoverc which of the following expressions are also true? a. dc+cb=db b. ad>db c. ad+cb=ab d. ad<cb

Algebra ->  Geometry-proofs -> SOLUTION: if c is the midpoint of aoverb and d lies on aoverc which of the following expressions are also true? a. dc+cb=db b. ad>db c. ad+cb=ab d. ad<cb      Log On


   

Question 669081: if c is the midpoint of aoverb and d lies on aoverc which of the following expressions are also true? a. dc+cb=db b. ad>db c. ad+cb=ab d. ad
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
looking at just the end points,
you have the line ab and c is the midpoint of it.
you have the line acb with the segments of ac equal to the segments of cb (equal length).
if d lies on ac, then d must lie between a and c.
that makes the whole line equal to adcb where d is between a and c.
this means that dc + cb = db
your line would look like this:
line:                  a----------d----------c--------------------b
length of dc                      d----------c
length of cb                                 c--------------------b
length of db                      d----------c--------------------b

since the whole is equal to the sum of its parts, the length of db has to be the length of dc plus the length of cb.
the statement that d is on the line ac implies that the point d lies somewhere between a and c.
that's my take.