Examples of Transitive Properties

Some of the most common transitive properties are listed as follows:

• Transitive Property of Equality
• Transitive Property of Inequality
• Transitive Property of Congruence
• Transitive Property of Angles

Let’s discuss these properties in detail as follows.

Transitive Property of Equality

One basic mathematical principle that pertains to equality connections is the Transitive principle of Equality. It says that two quantities are equal to each other if they are equal to a third quantity.

To put it symbolically, a = c is implied if b = c and a = b.

For instance,

• You may determine that x = y using the Transitive Property if x = 5 and 5 = y.

Transitive Property of Inequality

Transitive Property of Inequality states if a quantity is larger (or less than) a second, and a second quantity is bigger (or less than) a third, then the first amount is likewise greater (or less than) the third.

In sign language, it means that a > c if a > b and b > c. Likewise, it follows that a < c if a < b and b < c.

Note: Combining both properties for equality and Inequality, we can conclude

• a ≥ c if a ≥ b and b ≥ c
• a ≤ c if a ≤ b and b ≤ c

Transitive Property of Congruence

Similar to the Transitive Property of Equality, but exclusive to congruent geometric shapes, is the Geometric idea known as the Transitive Property of Congruence. When two figures are the same size and shape, they are considered congruent in geometry.

One geometric figure is congruent to another if and only if the second and third figures are likewise congruent, according to the Transitive Property of Congruence.

△ABC ≅ △XYZ if △ABC ≅ △DEF and △DEF ≅ XYZ

Transitive Property of Angles

In contrast to equality or congruence, the Transitive Property does not immediately apply to angles. There are other attributes, nonetheless, that you may utilize to infer angles while working with angle measurements and connections in geometry.

The Transitive Property of Angles, a particular use of the Transitive Property in relation to angle measurements, is one such property. According to the Transitive Property of Angles, the first angle is also equal to the third angle if one angle is equal to a second and a second angle is equal to a third.

∠A = ∠B and ∠B = ∠C implies that ∠A = ∠C.

For instance,

• According to the Transitive Property of Angles, ∠PQR = ∠VWX if ∠STU = ∠VWX and ∠PQR = ∠STU.
• It follows that ∠ABC = ∠GHI if ∠ABC = ∠DEF and ∠DEF = ∠GHI.

Read More

• Transitive Relations
• Transitive Relation on a Set 
• Properties of Equality
• Equivalence Relations

Transitive Property is a fundamental concept used when dealing with three or more quantities of the same kind related by some rule. Three elements are said to satisfy transitive property if a is related to the b by a certain rule, and the b is related to the c by the same rule, then we can definitely say that the a is related to the c by the same rule.

In simple words, if a implies b and b implies c, then a implies c. In this article, we will discuss all the topics related to Transitive Property including its definition, examples and various solved examples as well.