Thread: I think logic is messing with me.

1. 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!

2. Originally Posted by nathan02079
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