Question 54569This question is from textbook Geometry
: Could someone explain the difference between the Substitution property and the Transitive property? If you state that the measure of angle "A" is equal to 90 degrees, and the measure of angle "B" is equal to 90 degrees, then the measure of angle "A" = measure of angle "B" is proved by which property?
This question is from textbook Geometry
Answer by Born2TeachMath(20)   (Show Source):
You can put this solution on YOUR website! Wow! This is a doozy!!!
The substitution property is really a combination of a few properties, and is used when things are not in the correct order.
The TRANSITIVE PROPERTY states: If A = B and B = C, then A = C. Notice how the first equality ends with B while the second starts with B. If the "middler terms" are equal, then the "outside two" (A and C) are then equal to eachother using the TRANSITIVE PROPERTY.
In your problem, you have A = 90°, and B = 90°. Notice the order is wrong? In order for the TRANSITIVE PROPERTY to be used, the 90° must be in the "middle." So really, what we need to do first is apply the SYMMETRY PROPERTY (which states if X = Y, then Y = X) to reverse the order of the second statement, leaving A = 90° and 90° = B. Then we can use the TRANSITIVE PROPERTY to say that A = B.
Instead of doing these two steps, (SYMMETRY and then TRANSITIVE PROPERTIES), we short-cut the entire process and say that A = B and call it the SUBSTITUTION PROPERTY.
So SUBSTITUTION PROPERTY is really lazy math.
Therefore, use TRANSITIVE PROPERTY when things are lines up already ("middle terms are the same"), and use SUBSTITUTION PROPERTY when they are not.
I hope this helps! This is really only a big point in geometry. When you get to upper level algebra (adv alg, alg 2, trig, pre-calc, etc) we just call it the substitution property, and don't worry about the transitive property at all!
|
|
|
