Read the statements shown below:
If a closed figure has three line segments joined end to end, it is a triangle.
If all the three angles of a triangle are congruent, it is an equilateral triangle.
Morgan constructed a triangle with all three sides congruent in the geometry class.
Based on the given statements, which is a valid argument?

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- anonymous

t cannot be concluded that Morgan drew an equilateral triangle.
It can be concluded that Morgan drew a closed figure having three congruent line segments joined end to end.
It cannot be concluded that Morgan drew a closed figure having three line segments joined end to end.
It can be concluded that Morgan drew a rectangle.

- anonymous

- anonymous

Need help desperately

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## More answers

- anonymous

I think B

- anonymous

please verify me

- anonymous

- anonymous

I guess no one is going to help.

- anonymous

@mathmate you're my only hope

- anonymous

- anonymous

@mathmate what do you think?

- mathmate

@HareshGopal
Notice that the question says "based on the above statements".
I interpret it as, "based on the above statements ONLY", then we know that with three \(angles\) equal it is an equilateral triangle (correct name is equiangular triangle)
What morgan had was a triangle with three \(sides\) equal. So do you think we can drawa conclusion (based on the given statements ONLY?
We know we can prove that an equiangular triangle is equilateral, but that is not given.

- anonymous

I think it is b

- anonymous

- mathmate

Think of the question:
Given statement:
If I take a bus, I pay the fare.
Morgan takes a taxi.
\(Based~on~the~above~statements,\)
1. We cannot conclude that Morgan pays the fare.
2. We can conclude that Morgan pays the fare
3. We can conclude that Morgan has a lot of money.
4. We cannot conclude that Morgan has a lot of money.
What would be your answer?

- anonymous

none

- anonymous

- mathmate

What do you mean by none? No conclusion, or none of the choices?

- anonymous

@mathmate no conclusion

- anonymous

Oh I know @mathmate its a

- anonymous

to your example question

- mathmate

Can you now explain to me why it is a?

- anonymous

since she didn't go in the bus

- mathmate

Exactly.
The law of detachment says:
If the hypothesis is satisfied, the conclusion is true.
However, if the hypothesis (getting in a bus) is not satisfied, we cannot draw the conclusion (pay the fare), EVEN though we know (from outside the problem) that he pays the fare.

- anonymous

@mathmate so what about my question, am I correct?

- anonymous

(B)

- mathmate

Please prove the answer in words (not just the letter choice), and
please reread the question carefully!

- anonymous

This: It can be concluded that Morgan drew a closed figure having three congruent line segments joined end to end.

- anonymous

- anonymous

@mathmate ??????

- mathmate

The first statement says:
If a closed figure has three line segments joined end to end, it is a triangle.
the hypothesis is "a closed figure has three line segments joined end to end"
and the conclusion is "it is a triangle".
By the law of detachment, IF the hypothesis is true, then the conclusion (it is a triangle) is true.
The statement did not say that the converse is true.
The converse is:
If a figure is a triangle, then it is a closed figure has three line segments joined end to end
So we cannot assume that this last statement is true.
"Morgan constructed a triangle with all three sides congruent in the geometry class. "
only tells us that Morgan constructed a triangle.
Without the converse being true, we cannot conclude that:
"Morgan drew a closed figure having three congruent line segments joined end to end"
Therefore the statement
It can be concluded that Morgan drew a closed figure having three congruent line segments joined end to end.
is not logically true (unless the converse is true).

- anonymous

Ahh so It's A?

- anonymous

- anonymous

@mathmate i it cannot be concluded that Morgan drew an equilateral triangle.

- pooja195

@mathmate ...

- anonymous

@pooja195 do you think its that

- pooja195

im not good with this stuff ;-; sorry :(

- anonymous

- mathmate

@HareshGopal
I would agree with that, because Morgan drew three equal sides, and not three equal angles.

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