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

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Homework Help Overview

The problem involves four points A, B, C, and D in a plane and asks for correct statements regarding the relationship AB = BC + CD. Participants are exploring the implications of this equation in a geometric context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to identify which statements about the points and segments are correct based on the given equation. There is discussion around specific options, with some participants questioning the validity of their initial guesses and considering geometric principles like the parallelogram sum rule.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and reconsidering their answers. Some guidance has been offered regarding the geometric interpretation of the relationships between the segments, but no consensus has been reached on the correct statements.

Contextual Notes

Participants note a lack of clarity in their understanding due to insufficient explanation from the instructor, which may be affecting their ability to analyze the problem effectively.

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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.
 
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Why do you think it's C and D?
 
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.
 
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?
 
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.
 

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