Question

Make a two-column proof showing statements and reasons to prove that triangle NMT is similar to triangle PMN.

Answer 1

@ganeshie8

Answer 2

I have setup the reasons, i cant touch the statements

Answer 3

First thing I noticed was that I think its not just your statements that are incorrect, but your last 2 reasons also.

You did not include if any text was included with the picture such as what was given to you or what was proven. I say that your 3rd reason is incorrect because there is no evidence that <NTM is congruent to <PNM since no angles have been listed. I also have a feeling that you should place your 1st "Given" as your first reason and completely switch those two rows since usually we put the "Given" down first.

So first I would do:
[m<TNM is equal to m<NPT] - Given

Now try to use this information to figure out another angle, unless there is another given you are not telling me about or perhaps I was incorrect about the other given not being in existance since you did not list it down.

Answer 4

Im not supposed to change the statements, only the reasons

Answer 5

so what should be my order of reasons?

Answer 6

Ok then are you sure that statements 2 and 3 are given? I can guarantee you that statement 2 is given however the angles listed in statement 3 are not marked on the picture.

If you are only attempting to prove that these triangles are similar then it is clear that you only need to use the AAA similarity postulate. You listed this postulate on your 4th reason which means you made the correct decision. This leaves statements 1 and 3 left.

Since you claim that the statements were already pre-wrote then that means your order is fine for this moment. Just tell me whether or not statement 3 is actually a given statement.

Answer 7

all the statements were given, i can only chage the reasons

Answer 8

i put in all the reasons

Answer 9

When you list the term "given" as a reason, you are saying that you were already GIVEN the information. Usually they will TELL you what the given is or the picture will show it. This means that the reason for statement 3 cannot be given. After reviewing your picture once more, I am confident that statement 1 should be supplied with reason of "Given" or since you can just review the picture in order to understand that <NMT is indeed common to both triangles.

As for statement 3, you have already stated that Angle M is common to both triangle so that fufills one of the angle required to prove this statement. You have also proved that <TNM is congruent to <NPM which fufills another criteria. With this information, you can prove that <NTM is congruent to <PNM since both triangles need to equal 180. Both triangles have angles of 50 degrees and angle M which means that the remaining angles MUST be equal to each other so both triangles can achieve an accumulated interior degree sum of 180 degrees.

Answer 10

Si its given given given, then AAA? impossible

Answer 11

Just to try to sum up what I am trying to say:

Reason 1 should be Given
Reason 2 should be Given
Reason 3 should be Interior Angles must be 180 degrees. (You might have another term for this in class, I do not quite remember it. For this I would also recommend using a writing tool to write an explanation similar to mine.)
Reason 4 should be AAA Similarity Postulate


Reason 3 is NOT given.

Answer 12

How is reason 3 Interior angles must be 180 degrees?

Answer 13

I have just explained this to you. Angle M is inside both triangles, so think of angle M as only a variable that is included in both triangles. Both triangles also have an angle of 50 degrees inside each one. Think of this as an equation.

Angle M + 50 degrees + m<NTM = Angle M + 50 degrees + m<PNM

Subtract Angle M and 50 degrees from both sides and you will get
m<NTM = m<PNM

Does that help you understand better?

Answer 14

Altight Thanks! I appreaciate the help

Answer 15

Welcome