What is the difference between the substitution and transitive postulate?

Answer 1

No difference actually.
Sometimes the transitive postulate is stated as "Things equal to the same thing, or to equal things are equal to each other."

It is stated in algebra as "If a = b and b = c, then a =c."

Substitution says that if b =c then, then we may substitute c for b in the equation a =b getting a = c. This is the same result as given by the transitive postulate.

Sometimes one is easier to use one than the other.

Answer 2

Technically speaking, transitive property only applies to the situation a=b and b=c therefore a=c.

In substitution, you are taking something out and putting an equivalent thing in its place. Like this,

a + b = c and b=d, therefore a + d = c.

Notice, the second case does not follow the exact pattern that is transitive. Transitive property can also be extended to any length: z=y, y=x,x=w,w=v,v=t, therefore z=t. To do this by substitution would require multiple substitutions.

The difference is slight and a technicality, but a teacher can require you to use the correct one if he or she desires.

Answer 3

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RE:
What is the difference between the substitution and transitive postulate?

Answer 4

There are a couple differences, but in equations, they are often used interchangeably. In geometry, you have to use transitive if you have congruence statements because you are not talking about measures of angles or lengths of segments, you are talking about the set of points that makes up those objects. They are congruent, not equal. Substitution is used for values or variable that represent numbers (like AB means the length of segment AB, but AB with the bar over it means segment AB, the points that make up AB).

Also, you couldn't use transitive for something like this, it's just substitution:

If x+y = z and x = 30, then 30+y = z

I like to think of applying transitive when I have a "link" that connects the two equations or congruencies to each other. For example, If A = 40 and A = X+Y, then 40=X+Y. The two quantities are linked by A. Of course, substitution applies there too!

Answer 5

Substitution Property Of Congruence

Answer 6

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I don't see why you think it would be transitive. There are only two angles involved, here, not three. You need three for transitivity. They are simply substituting angle 1 for angle 3 because they are equal. By the way, both links you gave are for the same thing.

Answer 7

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