# The Transitive Property And Why You Need To Know It

Mathematics is a language that is structured by many properties.  One property that students need to comprehend is the Transitive Property.  Before we go any further let’s review the actual property.

Transitive Property: if a = b and b = c, then a = c

A few examples of the property

Example 1:   If 3 = (9/3) and   (9/3) = (30/10)  then 3 = (30/10)

Example 2:   if DC = FG and FG = HY then DC = HY

Hopefully you see that the property is pretty straight forward – it simply relates quantities that are equal but expressed differently.  The reason we learn such properties is to formally define common relationships in math.  Most students start to study specific math properties in middle school.  Usually the properties young math students first learn are about algebra and numbers.

However when students take high school geometry they will learn many, many more properties.  A big part of geometry is writing a mathematical proof and essential to that task is the application of describing relationships by specific properties.

Most students will have not experienced trying to write a proof before they take geometry.  As such many geometry students tend to dislike or find geometry challenging because writing proofs is much more abstract then the concepts taught in algebra.
The best way for students to help manage these new abstract challenges like writing a proof is to really make an effort to master the fundamentals. Hopefully this quick look at the Transitive Property demonstrates that the name of a property is often more intimidating than the actual concept.  So in the end don’t dismiss these properties as they will have increased importance as you study more complex mathematics.