# Transitive Property of Equality

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In mathematics, transitive property is the property which describes the relationship between variables based on logic statements of equality and inequality. There are two kinds of transitive properties, one for equality between variables and the other for inequality between variables. If there are three variables x, y, and z, and x is equal to y (x = y) and y is equal to z (y = z), then according to the Transitive property of equality, x is also equal to z (x = z).

Example 1: Given PQR is a triangle, and the measure of side PQ is equal to the measure of side QR. If the measure of side QR is equal to the side PR, then what is the relation between sides PQ and PR?

Given: side length of PQ= side length of QR

Side length of QR= side length of PR

Now to find the relationship between sides PQ and PR, we can use the Transitive property of equality.

Hence, according to the property:

side length of PQ= side length of PR

Example 2: The price of chocolate cupcakes is the same as the price of vanilla cupcakes and the price of vanilla cupcakes is the same as strawberry cupcakes. Now, what is the price of chocolate cupcakes in comparison with the price of strawberry cupcakes?

Given: price of chocolate cupcakes = price of vanilla cupcakes

Price of vanilla cupcakes = price of strawberry cupcakes

Now to compare the prices between chocolate and strawberry cupcakes, we can use the Transitive property of equality.

Hence, according to the property:

price of chocolate cupcakes = price of strawberry cupcakes!