Algebra 1 / Chapter 1: Addition And Subtraction / Basic Properties

Transitive Property of Equality

The Transitive Property of Equality is the following:

if the following are true:

  • a = b
  • b = c

then a = c

The Transitive Property of Equality is one of the most famous and useful properties in mathematics. This property is used in proofs of all shapes and sizes.

a, b, and c are all expressions, so they can be values, variables, operations, among others.

Examples

if the following are true:

  • x = y
  • y = 3

then x = 3

if the following are true:

  • i + 1 = j
  • j = k

then i + 1 = k

if (distance AB = distance XY) and (distance XY = 11), then distance AB = 11
Quiz (1 point)

Given that

0 + a = a + 0

and

a + 0 = a

What does the Transitive Property of Equality allow us to conclude?

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