Question

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?

Answer 1

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.

Answer 2

@ganeshie8

Answer 3

Need help desperately

Answer 4

I think B

Answer 5

please verify me

Answer 6

@mathmate @mathstudent55

Answer 7

@eyust707 @e.mccormick

Answer 8

I guess no one is going to help.

Answer 9

@mathmate you're my only hope

Answer 10

@misssunshinexxoxo

Answer 11

@mathmate what do you think?

Answer 12

@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.

Answer 13

I think it is b

Answer 14

@mathmate

Answer 15

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?

Answer 16

none

Answer 17

@mathmate

Answer 18

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

Answer 19

@mathmate no conclusion

Answer 20

Oh I know @mathmate its a

Answer 21

to your example question

Answer 22

Can you now explain to me why it is a?

Answer 23

since she didn't go in the bus

Answer 24

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.

Answer 25

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

Answer 26

(B)

Answer 27

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

Answer 28

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

Answer 29

@mathmate

Answer 30

@mathmate ??????

Answer 31

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).

Answer 32

Ahh so It's A?

Answer 33

@mathmate

Answer 34

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

Answer 35

@mathmate ...

Answer 36

@pooja195 do you think its that

Answer 37

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

Answer 38

@mathmate

Answer 39

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