The Transitive Property of Equality states that if a = b and b = c, then a = c. This property holds true for any mathematical expressions that can be equated, such as numbers, variables, or more complex equations. Here are two examples of equations that demonstrate the Transitive Property of Equality:
x + 5 = 9 and 9 = y - 2
x + 5 = y - 2
a^2 + 2ab + b^2 = (a+b)^2 and (a+b)^2 = a^2 + 2ab + b^2
a^2 + 2ab + b^2 = a^2 + 2ab + b^2
In both examples, by using the transitive property, we can conclude that x = y and (a+b)^2 = (a+b)^2 which both are same expressions.
In the first equation, we start with x + 5 = 9 and then 9 = y - 2. Since both sides of the first equation are equal to 9, we can substitute 9 for x + 5 in the second equation, giving us 9 = y - 2. This shows that the left side of the first equation is equal to the right side of the second equation, which is the Transitive Property of Equality.
In the second equation, we start with a^2 + 2ab + b^2 = (a+b)^2 and then (a+b)^2 = a^2 + 2ab + b^2, since both sides are the same then we can substitute (a+b)^2 for a^2 + 2ab + b^2 in the second equation, which results in (a+b)^2 = (a+b)^2. This shows that the left side of the first equation is equal to the right side of the second equation, which is the Transitive Property of Equality.
In summary, The transitive property states that if you have two expressions are equal to each other, and the second expression is equal to the third, then the first and the third expressions are equal to each other.