Proof in Algebra – Geometry Meets Algebra

In a previous blog post about proofs in algebra, I wrote about how to a geometric style proof to solving an algebraic equation. The video embedded into this post models how to justify the solving of an equation with a two-column proof and the justifying of two problems involving the segment addition postulate and the angle addition postulate. Introducing proofs with algebra makes sense. You build upon your knowledge of solving equations to learn the new skill of creating proofs.

To be able to write proofs effectively, you must know definitions, postulate, properties and theorems. As always, I hope this information in the video and blog is helpful. Feel free to comment or ask a question.

Geometry in Algebra – Using Proof in Algebra

You should be a student of geometry or algebra if you have found this post about using proof in algebra. If you are not a student of geometry or algebra, I encourage you to stick around and continue reading, you might just learn something. To effectively use proof in algebra and geometry, it is important to be familiar the properties of equality.

Properties of Equality

Properties of Equality

You should not forget about the distributive property of equality.

The Distributive Property

The Distributive Property

If you have taken algebra 1 or have experience solving equations, you already know these properties, but you are probably not used to naming them when solving an equation. This discussion about using proof in algebra is important, because many of the things you will asked to prove in geometry will involve solving equations, which is rooted in algebra. Here is an example of solving an equation in the form of a two-column proof.

Example – Justify each step in solving the equation (3x+5)/2 = 7.


Two Coloum Proof of Solving an Equation

Calling the problem above a proof is just a fancy way to say solve the equation. Instead of “showing your work” when solving the equation, you justify each new line, you use the two-column proof set up. Each step can be justified with a property of equality, which is seen in the reasons column of the two-column proof. Here is an example of solving a absolute value equation by “showing your work”. That is to say you are balancing the equation by performing the same operation to each side of the equation until the variable is isolated. Thus, the solution of the equation.

As has been seen with the segment addition postulate and the angle addition postulate, the use of algebra is integral. Without algebra, studying geometry would be more difficult. Most problems in geometry involve the use of algebra and learning how to “prove an algebra problem” will be a necessary part of making a proof in geometry, so, well it is a good idea to learn how to prove an algebra problem.

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