Transitive Property

Example 1: Ryan is 5 feet tall. If Ryan is of the same height as Evelyn, and Evelyn is of the same height as Barry, how tall is Barry?

Solution:

We can use the transitive property of equality here to find Barry’s height. 

Ryan’s height = Evelyn’s height

Evelyn’s height = Barry’s height

Ryan’s height = Barry’s height                  [Transitive property of equality]

5 ft = Barry’s height                                  [Substitute]

Hence, Barry is 5 feet in height.

Example 2: Find the value of b when a = b and a = 7.

Solution:

Here, it is given that a = b and the value of a is 7.

According to the transitive property of equality, if a = b and b = c then a = c.

Now, we can see that a = 7 and a = b. Thus, b = 7.

Hence, the value of b = 7.

Example 3: Find the value of x using the transitive property of equality.

x + 2 = z and z = \(x\text{ }+\text{ }2\text{ }=\text{ }z\text{ }and\text{ }z\text{ }=\text{ }3\)

Solution:

\(x\text{ }+\text{ }2\text{ }=\text{ }z\)                          [Given]

\(z\text{ }=\text{ }3\)                                   [Given]

\(x\text{ }+\text{ }2\text{ }=\text{ }3\)                          [Transitive property of equality]

\(x\text{ }+\text{ }2\text{ }-\text{ }2\text{ } =\text{ }3\text{}-\text{ }2\)          [Subtracting 2 from both sides]

\(x \text{ } = 1\)                                    [Simplifying]

Hence, the value of x is 1.

Example 4: Rose prepared 3 fruit baskets. The first basket weighs more than the second basket and the second basket weighs more than the third basket. Which basket is the heaviest?

Solution:

First basket’s weight > Second basket’s weight

Second basket’s weight > Third basket’s weight

Applying transitive property of inequality,

First basket’s weight > Third basket’s weight 

So the first basket weighs more than both the second and third baskets.

Hence, the first basket is the heaviest.