Proof Check: Geometry AB=EF If A=/B

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To prove that line AB equals line EF given that points A and B are distinct, it is established that two distinct points determine a unique line. The discussion clarifies that if A and B are on line EF, then the line formed by these points, denoted as X, must intersect line EF, denoted as Y, at two distinct points. This intersection implies that lines X and Y are the same, leading to the conclusion that AB equals EF. The sufficiency of this proof is questioned, prompting further clarification on the definitions and assumptions regarding points A and B. Overall, the argument hinges on the axiomatic properties of lines and points in geometry.
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Homework Statement



Let A and B be elements of the line EF such that A=/B prove that the line AB=EF

Homework Equations



Axiom that two points determine a unique line and that the intersection of two lines has two distinct points then these lines are the same.

The Attempt at a Solution


[/B]
If A and B are two distinct points they then determine a unique line say X. Let EF=Y then the intersection of X and Y contains at least two distinct points therefore X=Y so AB=EF. Is that sufficient?
 
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Loststudent22 said:

Homework Statement



Let A and B be elements of the line EF such that A=/B prove that the line AB=EF
What do you mean by A=/B?

Are A and B points in the line segment EF?
Loststudent22 said:

Homework Equations



Axiom that two points determine a unique line and that the intersection of two lines has two distinct points then these lines are the same.

The Attempt at a Solution


[/B]
If A and B are two distinct points they then determine a unique line say X. Let EF=Y then the intersection of X and Y contains at least two distinct points therefore X=Y so AB=EF. Is that sufficient?
 

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