Proofs help.

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Hi everyone,I've decided to learn math as a goal but am in desperate need of help.Here is a proof in which I'm a bit confuse about because of the way my text book solves it and the conclusion I came up with.My question is,can both be right?Also in my book it describes the segment addition postulate as,if b is between A and C then AB plus BC =AC while that is true and I understand.But, I'am confuse because the online definition is that EQUAL QUANTITIES ADDED TO EQUAL QUANTITIES will be equal, and they also have something call partition postulate which describes what my text definition for addition postulate perfectly.


prove=M1=M3
xvz=yvw = given
xvz=m1 +m2 +yvw=m2+m3=angle addition postulate
M1+m2=m2+m3=substitution property of equality
m2=m2 =reflexive axiom of equality
m1=m3= subtraction property of equality

My proof
xvz=yvw=given
m2=m2= reflexive axiom
xvz-2=yvw-2=subtraction property of equality
xvz-2=xyv yvw-2=zvw=angle subtraction postulate
1=3=substitution postulate

 

[Steven G]

Hi everyone,I've decided to learn math as a goal but am in desperate need of help.Here is a proof in which I'm a bit confuse about because of the way my text book solves it and the conclusion I came up with.My question is,can both be right?Also in my book it describes the segment addition postulate as,if b is between A and C then AB plus BC =AC while that is true and I understand.But, I'am confuse because the online definition is that EQUAL QUANTITIES ADDED TO EQUAL QUANTITIES will be equal, and they also have something call partition postulate which describes what my text definition for addition postulate perfectly.


prove=M1=M3
xvz=yvw = given
xvz=m1 +m2 +yvw=m2+m3=angle addition postulate
M1+m2=m2+m3=substitution property of equality
m2=m2 =reflexive axiom of equality
m1=m3= subtraction property of equality

My proof
xvz=yvw=given OK (but write angle xvz...)
m2=m2= reflexive axiom OK
xvz-2=yvw-2=subtraction property of equality OK-write angle xv-angle 2
xvz-2=xyv yvw-2=zvw=angle subtraction postulate OK (xyv should be xvy)
1=3=substitution postulate OK







View attachment 4886

Yes, when EQUAL QUANTITIES are ADDED TO EQUAL QUANTITIES the result will be equal. There is another saying that says the sum of the parts equal the whole.

You have a line segment AC. This is a 'line' drawn from point A to point C. Now on this line segment is a point B ( B is between A and C). So we can break up the segment AC into two parts, namely AB and BC. So we can say something like AB + BC =AC. Unless I am missing something we are not adding equals to equals.

 

[box]

Yes, when EQUAL QUANTITIES are ADDED TO EQUAL QUANTITIES the result will be equal. There is another saying that says the sum of the parts equal the whole.

You have a line segment AC. This is a 'line' drawn from point A to point C. Now on this line segment is a point B ( B is between A and C). So we can break up the segment AC into two parts, namely AB and BC. So we can say something like AB + BC =AC. Unless I am missing something we are not adding equals to equals.

Ah thank you for the help,I was just in a rush as the question was bothering me alot.So,I didn't really proof read properly,but you get my point.Thanks again for the help.Now I know that there can be more than 1 conclusion to a proof.
Edit-What did u mean by not adding equals to equals?The first proof which uses angle addition postulate was from my textbook if that is what you meant.

 

[Ishuda]

There are usually many ways to prove the same thing and as long all proofs reach the same conclusion things are fine. It is not unusual for there to be different names for the same thing, especially if you are talking about two different field of mathematics. For example "the segment addition postulate" when talking about geometry and, in particular lines, and the "partition postulate" which also may deal with lines and, in that case, tends to be talking about the real number line. Also, sometimes the name will change over the course of time.

Because of your image, your proof is understandable and is, IMO, a good proof.

 

[box]

There are usually many ways to prove the same thing and as long all proofs reach the same conclusion things are fine. It is not unusual for there to be different names for the same thing, especially if you are talking about two different field of mathematics. For example "the segment addition postulate" when talking about geometry and, in particular lines, and the "partition postulate" which also may deal with lines and, in that case, tends to be talking about the real number line. Also, sometimes the name will change over the course of time.

Because of your image, your proof is understandable and is, IMO, a good proof.

Thank you sir,very motivating to know that I'm heading in the right direction.