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.

proof-in-algebra-pilarski

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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7 Responses

  1. [...] Geometry in Algebra – Using Proof in Algebra [...]

  2. [...] two column proof, paragraph proof and a flow proof. Personally, I am most comfortable a creating a two column proof or a  paragraph [...]

  3. I have long thought that Algebra 1 should be taught this way. I’m excited to see that I’m not alone. Next year I get to put it into practice because I’ll be teaching Algebra 1.

    • Waski,

      I have not taught Algebra as proof in my Algebra 1 class. I have only used teaching algebra as a means to introduce proofs in geometry. I look forward to hearing from your experience teaching algebra as proofs. Do you plan on using a blog at all?

      Regards,

      Mr. Pi

  4. i like how the examples are broken down. that’s how i imagined it to be.

  5. they skipped a lot of steps..

    • I am not sure what you mean by, “they skipped a lot of steps..?”

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