# Which statement is true?

#### starmoonsun101

##### New member
I think the answer is 1 or 4, but I'm not sure.

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#### Dr.Peterson

##### Elite Member
I think the answer is 1 or 4, but I'm not sure.
Tell me why you think 1 is true, and why you think 4 is true. Then decide which is more convincing.

Math is not about "thinking" in the sense of "feeling", but about genuine thinking, which means reasons. Let's hear them!

#### starmoonsun101

##### New member
I'm not really sure why I thought 1. But I thought 4 because inscribed angles that intercept the same arc or congruent arcs of a circle are congruent.

(I need help before 9pm, so 3 hours)
Thank you

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#### Dr.Peterson

##### Elite Member
I'm not really sure why I thought 1. But I thought 4 because inscribed angles that intercept the same arc or congruent arcs of a circle are congruent.

(I need help before 9pm, so 3 hours)
Thank you
So, are the arcs intercepted by angles ABC and BCD congruent? If so, then you know.

As for 1, what congruent things are those chords associated with?

You may find it helpful to mark on the picture the given congruent arcs, and then one by one mark (in a different color) the things claimed in each option, so you can compare them. Sometimes you need a chain of relationships to make a conclusion, but for this everything takes a single step.

#### pka

##### Elite Member
I think the answer is 1 or 4, but I'm not sure.
I find that it is interesting that of the four possible answers, there is a subset of three in which each one implies the other two. That means that the three are all equivlent.

#### starmoonsun101

##### New member
So, are the arcs intercepted by angles ABC and BCD congruent? If so, then you know.

As for 1, what congruent things are those chords associated with?

You may find it helpful to mark on the picture the given congruent arcs, and then one by one mark (in a different color) the things claimed in each option, so you can compare them. Sometimes you need a chain of relationships to make a conclusion, but for this everything takes a single step.
I'm not sure if the arcs intercepted by the angles ABC and BCD are congruent?

#### starmoonsun101

##### New member
So, are the arcs intercepted by angles ABC and BCD congruent? If so, then you know.

As for 1, what congruent things are those chords associated with?

You may find it helpful to mark on the picture the given congruent arcs, and then one by one mark (in a different color) the things claimed in each option, so you can compare them. Sometimes you need a chain of relationships to make a conclusion, but for this everything takes a single step.

Is the answer 1, because they are corresponding chords to the congruent arcs?

#### pka

##### Elite Member
Is the answer 1, because they are corresponding chords to the congruent arcs?
Is there a theorem to that effect that you have learned?

#### starmoonsun101

##### New member
Is there a theorem to that effect that you have learned?
I believe so.

#### starmoonsun101

##### New member
Is there a theorem to that effect that you have learned?
Does this theorem apply to this circle?

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#### starmoonsun101

##### New member
Do you know that is or do you just believe that is?
This is the theorem we were given. Does this theorem apply to this circle?

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#### Jomo

##### Elite Member
I can not believe this post. I made up a video showing the solution. It will be removed in a few days unfortunately.
You can view the video here

#### Dr.Peterson

##### Elite Member
I'm not sure if the arcs intercepted by the angles ABC and BCD are congruent?
This is the point of a question like this. They are asking if it is necessarily true, based on the given fact -- not if it might be true, or if you think it's true. You correctly state that you're not sure; in fact, just looking at the picture, you clearly have an example in which it is not true. (Just measure the angles.)

So you can't say it is true.

As for #1, you've shown a theorem that says, if the arcs are congruent, then the chords are congruent; and you are told that the arcs are congruent. From this, you can conclude that the chords are congruent. That is a proof. So you can say that you know #1 is true.

Do you understand?

#### starmoonsun101

##### New member
This is the point of a question like this. They are asking if it is necessarily true, based on the given fact -- not if it might be true, or if you think it's true. You correctly state that you're not sure; in fact, just looking at the picture, you clearly have an example in which it is not true. (Just measure the angles.)

So you can't say it is true.

As for #1, you've shown a theorem that says, if the arcs are congruent, then the chords are congruent; and you are told that the arcs are congruent. From this, you can conclude that the chords are congruent. That is a proof. So you can say that you know #1 is true.

Do you understand?

Yes, I understand. Thank you for the explanation!

#### starmoonsun101

##### New member
I can not believe this post. I made up a video showing the solution. It will be removed in a few days unfortunately.
You can view the video here
Thank you for the explanation!

Also, did you make that video to help me, or was it just a coincidence that we had the same problem?

#### Jomo

##### Elite Member
Thank you for the explanation!

Also, did you make that video to help me, or was it just a coincidence that we had the same problem?