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Reflexive Property

This property might seem obvious, but it is very important. It is one of the fundamental truths that makes all math work.

The reflexive property of equality says a number is equal to itself. $$a=a$$

The reflexive property is like looking in a mirror. Whatever you place in front will be shown in the reflection.

This is true of any number, real or imaginary.

$$2=2\\ 4i=4i$$

This is also true of variables, given it is the same variable written in the same equation.

$$x=x\\ 15y=15y\\ 10r^2=10r^2$$

Reflexive Property of Equality

The Reflexive Property of Equality, along with the Symmetric and Transitive Properties of Equality, are some of the most important properties in math. It is also used to justify the Addition/Subtraction and Multiplication/Division Properties of Equality, ad well as the Additive and Multiplicative Identity Properties

Here is a graphic stating the Reflexive Property of Equality:

In other words, any number or quantity, even if it has variables, is equal to itself!

For example: $$x=x$$ $$2=2$$ $$r^2+s=r^2+s$$

One way to remember the Reflexive Property of Equality is to think about the words reflexive or reflection. If you look at your reflection in a mirror, you see yourself! Likewise, by the Reflexive Property, any number is its own mirror image. Any number (such as a real number) is equal to itself!

(Video) What is the Reflexive Property of Equality?

by tarveracademy

This video by TarverAcademy discusses the reflexive property of equality using a side of a triangle.

$\large{\text{Summary}}$

The reflexive property says a number is equal to itself. $$a=a$$ The video above discusses how this property is most important when looking at congruent shapes (like triangles).

If two triangles share a line segment, we can use the reflexive property to state that the shared line segment is one side of the first triangle, and that line segment is also equal to one side of the second triangle.