Transitive Properties – The Transitive and Substitution Properties

The Transitive and Substitution Properties

The Transitive properties are the same as algebra. So if you have come in contact with the below formula of algebra then you are not far from the transitive properties. If a = b and b = c, then a = c. it is the same as transitivity. But what then is substitution? Substitution is, a = b and b < c, then a < c. let’s look into the theorems (algebra express in symbols or formula) in full details.

Transitive Properties

  • Transitive Property for three segments or angles

This is typically a three segments or angles of transitive whereby if two segments or angles are congruent to the third segment or angle, then they are congruent to each other. There is also a transitive property for four segments of angles.   Let look at this illustration of the two-segment properties of transitive.

This above figure is a typical illustration of the transitive property of three-segment or angles.

  • Transitive Property for Four segments or angles

Assuming two angles are congruent to other congruent angles, thus they are said to be congruent to each other. This is typically how four-segment or angles looks like.Transitive Properties

The above illustration is the transitive property for four segments.


  • Substitution Property

Assuming two segments or angle are congruent and as a result, you had a statement involving one of them, thus, you can pull the reversal one and replace the one with the other.Transitive Properties


We have set out tips or guideline that will help you figure out the Transitive and Substitution properties without mixing them up. Therefore, if you are ready, follow the below guide.

  1. Ensure to use the Transitive properties as the reason in a proof when a statement on the same line involves congruent angles.
  2. Make use of the substitution property when the statement does not involve a congruence.

Check out for the below proof from a TGFI rectangle!Transitive Properties

Transitive Properties Statement 1:Transitive Properties

Thus, the reason for statement 1 is Given.

Statement 2:

Transitive Properties

The reason for statement 2: whenever two angles form a right angle, it means that they are complimentary. Therefore, it defines complementary.

Statement 3:Transitive Properties

Thus, the statement for statement 3 Given.

Statement 4:Transitive Properties

What happened over the statement 4 is shows substitution property. Statement 2 and 3; whereby angle 2 replaces 1.

Take a look at the proof for the final segment of the program.Transitive Properties

Statement 1:

Reason for statement 1: Given.Transitive Properties

Reason for statement 2: A midpoint divides a segment into two congruent segments.Transitive Properties

Reason for statement 3: Given.Transitive Properties

Reason for statement 4: Transitive Property (for four segments; statements 2 and 3).


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