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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] Determine whether the statement is a valid definition: If an angle is a right angle, then its measure is greater than that of an acute angle.

Thorin T (Tutor)

[00:00:07] Hi there!
Welcome to Tutor.com .

Guest (Customer)

[00:00:13] Hi

Thorin T (Tutor)

[00:00:20] I see you have a simple question... :)

Guest (Customer)

[00:00:29] yeah

Thorin T (Tutor)

[00:00:33] What do you think of it so far?

Guest (Customer)

[00:00:44] we have to do something with a biconditional statement and it's kinda confusing

Thorin T (Tutor)

[00:00:59] Ah.
I think I see where this is going...

Guest (Customer)

[00:01:09] so to make it a true biconditional statement the conditional and converse has to be true

Thorin T (Tutor)

[00:01:17] A biconditional statement is in the form A if and only if B, correct?

Guest (Customer)

[00:01:27] yeah

Thorin T (Tutor)

[00:01:33] Well, let's try that for this one.

[00:02:02] What if we reverse the two propositions here?

Guest (Customer)

[00:03:05] it would be: the measure of an acute angle is greater if and only if its a right angle

Thorin T (Tutor)

[00:03:29] That's not quite right...

[00:03:36] It would be more like...

[00:03:53] If an angle's measure is greater than an acute angle, it is a right angle.

Guest (Customer)

[00:04:13] yeah

[00:04:15] ok

Thorin T (Tutor)

[00:04:31] So, is that statement true?

Guest (Customer)

[00:04:54] i don't think so

[00:05:04] because there is obtuse

[00:05:09] and straight

Thorin T (Tutor)

[00:05:11] Exactly!

[00:05:19] An obtuse angle is a counterexample...

[00:05:28] In fact, even acute angles are larger than other acute angles.

[00:05:45] So the converse is false.

Guest (Customer)

[00:06:09] how would you put the "if an angle's measure is greater than an acute angle, it is a right angle" into a biconditional statement

[00:06:15] with the "if and only if"

Thorin T (Tutor)

[00:06:17] Well, you could say...

[00:06:41] An angle is right if and only if it its measure is greater than that of an acute angle.

[00:07:17] Obviously, that statement is also false.

Guest (Customer)

[00:07:37] oh k

Thorin T (Tutor)

[00:07:44] What about the original statement?
Is it true?

Guest (Customer)

[00:08:20] yeah

[00:08:27] but the converse statement is not true

[00:08:32] so that makes it false?

Thorin T (Tutor)

[00:08:33] Yes, because any right angle is greater than any acute angle.

[00:08:36] What it means is...

Guest (Customer)

[00:08:39] b/c they both have to be true?

Thorin T (Tutor)

[00:08:40] It's a true statement...

[00:08:48] ...but it's NOT a valid definition.

[00:09:02] It's just a characteristic of right angles, but it doesn't define them.

Guest (Customer)

[00:09:05] Oh

[00:09:14] i get it

Thorin T (Tutor)

[00:09:22] Good!

[00:09:34] I guess the point here is that valid definitions need to be biconditionally true statements.

[00:09:44] It's not enough for them just to be true.

[00:10:00] Make sense?

Guest (Customer)

[00:10:07] yeah

[00:10:14] i have another question

[00:10:17] problem

Thorin T (Tutor)

[00:10:19] Okay!
Let's see it.

Guest (Customer)

[00:10:32] If two rays are opposite rays then they have a common endpoint

Thorin T (Tutor)

[00:10:49] Do you need to decide whether it's true, or biconditionally true?

Guest (Customer)

[00:11:06] i need to decide if its a valid definitions

Thorin T (Tutor)

[00:11:18] A definition of what term?

Guest (Customer)

[00:11:30] opposite ray

Thorin T (Tutor)

[00:11:43] All right.
First, is this statement true?

Guest (Customer)

[00:11:54] yeah

Thorin T (Tutor)

[00:11:58] Sure.

[00:12:06] Next, what about its converse?

[00:12:35] What do we get if we switch the antecendent and consequent?

Guest (Customer)

[00:12:38] yeah i think it is true

Thorin T (Tutor)

[00:12:51] Can you write the new converse sentence? :)

Guest (Customer)

[00:13:14] if they have a common endpoint, then they are opposite rays

Thorin T (Tutor)

[00:13:21] Watch out for words like 'they'...

[00:13:25] What is they?

[00:13:41] We haven't defined it yet.

Guest (Customer)

[00:13:54] oh

[00:14:06] if two rays have a common endpoint, then those two rays are opposite rays

Thorin T (Tutor)

[00:14:17] Good.
Although we can leave the second 'they' in. :)

Guest (Customer)

[00:14:27] oh ok

Thorin T (Tutor)

[00:14:52] Now that we have it written out...does it seem true?

Guest (Customer)

[00:15:06] yeah

Thorin T (Tutor)

[00:15:23] I just drew two rays!

[00:15:37] Do they have a common endpoint?

Guest (Customer)

[00:15:46] yeah

Thorin T (Tutor)

[00:15:48] Are they opposite rays?

Guest (Customer)

[00:15:58] oh.. no

Thorin T (Tutor)

[00:16:08] Then that's the trick.

[00:16:14] Opposite rays need to lie in a straight line.

[00:16:24] So the converse statement is FALSE.

Guest (Customer)

[00:16:43] oh i get it

Thorin T (Tutor)

[00:16:44] Cool. :)

Guest (Customer)

[00:16:48] :)

Thorin T (Tutor)

[00:16:49] So, is this a valid definition?

Guest (Customer)

[00:16:57] No

Thorin T (Tutor)

[00:17:03] No indeed.

[00:17:20] If it said, "are opposite rays in a straight line", then it would be.

[00:17:26] But it left that part out.

[00:17:43] Or, rther...

[00:18:01] If it said, If two rays are opposite rays, then they have a common endpoint AND lie in a straight line.

[00:18:09] That would define "opposite rays".

Guest (Customer)

[00:18:20] Oh

Thorin T (Tutor)

[00:18:36] Because the converse is also true.

[00:18:44] Oh, except...

[00:18:55] They need to actually go in opposite directions...

[00:19:06] So we could say "form" a straight line, instead of "lie in".

[00:19:21] But that's just a detail.

[00:19:26] I think you get the idea. :)

Guest (Customer)

[00:19:38] yeah

[00:19:42] ThankS so much!!!

Thorin T (Tutor)

[00:19:44] Okay!
You're welcome!

Guest (Customer)

[00:19:46] YOu were a BIG help!

Thorin T (Tutor)

[00:19:49] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

[00:19:52] I'm glad :)

[00:19:57] Have a good afternoon!

Guest (Customer)

[00:20:03] Thanks!

Thorin T (Tutor)

[00:20:02] And good luck with the rest of these.

Guest (Customer)

[00:20:04] You too!

Thorin T (Tutor)

[00:20:06] Bye now!

Guest (Customer)

[00:20:11] Thanks!