"If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ?

[Leo34005]

1. The problem statement, all variables and given/known data

"If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ?

2. Relevant equations

A) Symmetric property of equality
B) Substitution property of equality
C) Addition property of equality
D) Subtraction property of equality
E) Reflexive property of equality

3. The attempt at a solution

I think its C)

because that says that if e + x = m and f + x = m then e must equal f

[Hurkyl]

because that says that if e + x = m and f + x = m then e must equal f
However, the statement under consideration:
"If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ?
says
if e+x=m and e=f, then f+x must equal m
so it's not a match.

[Leo34005]

So its an example of the Symmetric property of equality

[Hurkyl]

Well, what pattern is that property?

[Leo34005]

Addition

[VietDao29]

So its an example of the Symmetric property of equality

Symmetric property of equality says that: If A = B, THEN B = A, i.e the order does not matter, you can interchange the LHS (left-hand side), and the RHS (right-hand side).

No, read again..

"If AB+BC = 24 and AB = 10, THEN 10 + BC = 24 is an example of the ?"

In the problem, do you realize what you are doing with AB, and 10?

Addition

Please, don't play guessing game here. Mathematics is not for guessing..

[Leo34005]

substituting? so its the Substitution property of equality

am i right?

[VietDao29]

substituting? so its the Substitution property of equality

Are you sure? How many percent sure? :-" And may I ask you why you are choosing that option?

[Leo34005]

Ok then.

If Substitution property of equality is not the answer , THEN Addition property of equality is.

I need confirmation, is it right?

[VietDao29]

Ok then.

If Substitution property of equality is not the answer , THEN Addition property of equality is.

:))

Ok man.

As I told you before mathematics is not a guessing subject. Unless you really want to understand (by giving out questions about where you are not sure, or simply tell me, why you are choosing that option), instead of guessing like that, I won't confirm your answer. :)

Please acknowledge that, confirming answers like this is not much different from giving out solutions, which is against the forums' rules.

[NJunJie]

The answer is quite obvious.
Yep. Maths is not a game! we don't make substitutions in life to get an answer :P

[symbolipoint]

VietDao29 and I agree. Do not guess. Learn the properties. You have these to choose from:
A) Symmetric property of equality
B) Substitution property of equality
C) Addition property of equality
D) Subtraction property of equality
E) Reflexive property of equality
Those are like the identities or names for the properties. Read what each one means in its formal statement. COMPARE your example to each of these properties. Which one fits? What does each property allow you to do with numbers and values?

By the manner of your question, you must be studying Geometry. Your numbers are lengths of segments. The question you ask about relates to segments and parts of segments AND relates to the number properties of equality, one of which you are supposed to choose.

You should refer to the formal statement of each number property in your textbook to identify the property which is used in your original question. You learned them when you studied introductory algebra.