What are the correct statements for AB=BC+CD in a plane with 4 points?

[Whiz]

Homework Statement

If A, B, C, D are 4 points in a plane, then find ALL correct statements if AB=BC+CD

A. AB is parallel to BD
B. AB+BC=CD
C. AB=BD
D. AB−BC=BD
E. none of the above

[Note: The answer could be more than one option]

Homework Equations

None

The Attempt at a Solution

I'm not quite sure how to do this question, even though it seems easy. I'm thinking option C and D but it's wrong. I'm pretty much doing guess work here because my instructor didn't explain it.

Can I get some help here? Thanks in advance.

 

[Office_Shredder]

Why do you think it's C and D?

 

[Whiz]

After some consideration, I think D is incorrect. But I chose C because a friend told me to use the parallelogram sum rule (AR = AP + PR).

So my new guess would be just C. I'm not sure how to check A though.

 

[Mark44]

For A, draw a line segment from B to C, then draw another line segment from C to D. Then you know that BD = BC + CD. You're given that AB = BC + CD. Can you conclude anything from these two equations?

 

[HallsofIvy]

From AB= BC+ CD, subtracting BC from both sides, you get AB- BC= CD, not BD.

Yes, vector addition can be visualized as the "parallelogram rule". That gives the correct answer.