MHB Prove 1 & 2: Bisector Properties of Angles

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SUMMARY

The discussion centers on proving that an angle has only one bisector, specifically addressing two key points: (1) there exists only one bisector for a specific angle, and (2) each angle uniquely corresponds to one bisector. The reasoning provided is that an angle α has a single bisector because it yields only one value for α/2, analogous to how a number has a unique half. This establishes the fundamental property of angle bisectors in Euclidean geometry.

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  • Study the properties of angle bisectors in Euclidean geometry.
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highmath
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How can (1) I prove that there is only one bisector of a angle to only one specific angle
and
(2)There is only a specific angle with only one bisector of it.
 
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I think your question needs clarification - perhaps a diagram? Can you be more specific? As it is, a line may bisect infinitely many angles, I believe.
 
What will happen if a angle has more than one bisector?
What will happen if some angles have more than one bisectors and other not?

What is the reason that angle has only one bisector?
 
highmath said:
What is the reason that angle has only one bisector?

An angle $\alpha$ has only one bisector because there is only one possible value for $\frac{\alpha}{2}$.
 
It seems to me to be similar to asking if, for any particular number, are there multiple values that are half of that number. For example, we know 6 is half of 12...can you think of another number that is half of 12?
 

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