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Thread: I think logic is messing with me.

  1. #1
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    I think logic is messing with me.

    I was given two diagrams and explanations.



    Given: $\displaystyle \angle1=\angle2$
    Implies: $\displaystyle AB=CD$ and $\displaystyle arc(AB)=arc(CD)$

    Given: $\displaystyle AB=CD$
    Implies: $\displaystyle \angle1=\angle2$ and $\displaystyle arc(AB)=arc(CD)$

    Given: $\displaystyle arc(AB)=arc(CD)$
    Implies: $\displaystyle \angle1=\angle2$ and $\displaystyle AB=CD$


    Given; $\displaystyle AB$
    Implies: $\displaystyle \angle1=\angle2$

    Given: $\displaystyle arc(AB)$
    Implies: $\displaystyle \angle1=\angle2$

    Now I have to explain:

    1. Why is $\displaystyle \angle1$ equal to half of $\displaystyle arc(AB)$?
    2. Why is $\displaystyle \angle2$ equal to half of $\displaystyle arc(CD)$?
    3. If $\displaystyle \angle1=\angle2$, what can you say about $\displaystyle arc(AB)$ and $\displaystyle arc(CD)$? Why?

    Like, I know the rules. I see the pictures, it's just there. It's always implied. Always the case. But I can't really EXPLAIN it or put it in words. It's so frustrating!

    Any help is appreciated. Thanks!
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  2. #2
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    Quote Originally Posted by nathan02079 View Post
    I was given two diagrams and explanations.

    ...

    Now I have to explain:

    1. Why is $\displaystyle \angle1$ equal to half of $\displaystyle arc(AB)$?
    2. Why is $\displaystyle \angle2$ equal to half of $\displaystyle arc(CD)$?
    3. If $\displaystyle \angle1=\angle2$, what can you say about $\displaystyle arc(AB)$ and $\displaystyle arc(CD)$? Why?

    Like, I know the rules. I see the pictures, it's just there. It's always implied. Always the case. But I can't really EXPLAIN it or put it in words. It's so frustrating!

    Any help is appreciated. Thanks!
    Have a look here: Inscribed angle - Wikipedia, the free encyclopedia
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