Geometry help!?

Question

this is the problem...


given: B is the midpoint of (line segment) AC
prove: AB + CD = BD
then it shows a picture of a line with points A,B,C, and D..in that order evenly spread out.

I HATE PROOFS!
someone please help me!!

Thats all the problem tells me
sorry =/

Answer 1

I don't know the names of the justifications, but here's the basic idea:

AB=BC <-midpoint rule, if b is the midpoint it splits into 2 = sections
BC+CD=BD (can be seen on the picture, rule of addition??)
AB+CD=BD <-transitive/substitution property (look at the first step)

Answer 2

Listen to Jon D. His answer is correct.
I'm not sure why everyone else finds the problem so confusing. You described the diagram pretty well, and the problem makes perfect sense.

Jon D used some shorthand. Here is his proof with a few words added to help you:

AB=BC <-midpoint rule, if B is the midpoint it splits AC into 2 equal line segments

BC+CD=BD (can be seen on the picture, rule of addition??)
Another way to express the reason for this statement is:
The whole is equal to the sum of its parts (and is greater than any one of them).

AB+CD=BD <-transitive/substitution property (look at the first step)
You could simply say:
by substitution of AB for BC, since we earlier showed that
AB = BC

Answer 3

I don't believe you were given enough information. The only thing you know for certain is that AB = BC. Notwithstanding the picture which seems to indicate that points A, B, C, and D are 'evenly
spread out', there is nothing in the problem that gives any concrete information about the length of CD.

Answer 4

if B is the mid point of line segment AC then
AB+BC=AC
we can go only thus far with the information provided

Answer 5

One cannot answer the question unless you tell us where D is...