Ask Education: Getting into the Geometry Mindset

Dec 9, 2021 | Location Point Loma

 

Hi, Mathnasium. I did really well in Algebra 1, and I really liked it. But now that I’m in Geometry, I’m struggling to understand it. It almost feels like a foreign language. Do some people just not get Geometry? Is it supposed to seem different than regular math? And what can I do so that it makes more sense to me?

~Kira L.
10th Grade

Thanks for the question, Kira. Let us start by saying that your concern is not uncommon; unfortunately, there is a misconception that students who do well in Algebra will not do well in Geometry and vice versa. We are here to tell you that is not the case. You (and students everywhere) are capable of “getting” Geometry!

Algebra vs. Geometry

Because the study of Algebra builds on analytical thinking, the misconception is that Algebra relies solely on the left side of the brain. However, at some point, Algebra requires the use of both sides of the brain, and this is where you have an opportunity to prepare for the type of spatial thinking required in Geometry.

Geometry is the branch of mathematics that deals with the properties, measurement, and relations of points, lines, angles, surfaces, and solids. Geometry focuses on spatial reasoning and on understanding vocabulary, knowing facts, and using logic to express relationships and establish what things are true.

The Connection

Geometry, much like Algebra, relies on using both the right and left sides of the brain. So, in a mind that understands Algebra, there is plenty of room to also understand Geometry. For example, in coordinate geometry, you apply the visual representations from Algebra, namely graphing relations and functions.

Creativity helps you visualize a problem, reconceive it, and construct drawings to solve problems, but analytical thinking helps you compute and prove. Geometry and Algebra bring together both worlds. The first few steps to solving practical Geometry problems and Geometric proofs comprise of drawing diagrams, recording measurements and units, dividing figures into manageable portions, and identifying geometric relationships. The subsequent steps necessitate the use of analytical and logical skills primarily built in Algebra. For example, when solving a Geometric proof, you follow a logical order to reach a conclusion, similar to the series of steps you take to solve an Algebraic equation.

Next Steps

So, now let’s talk about the next steps you can take to help Geometry make more sense.

Familiarize yourself with Algebra and Geometry vocabulary, axioms, and theorems. The study of Geometry is filled with new terms and “truths” specific to angles, surfaces, and solids. Learning the definitions, symbols, and facts will take time, and we recommend keeping a running list of them. Consider these categories:

Properties: Parallel lines, proportional segments, distance, polygons, circles, angle measurement, ratio and proportion, and triangles (similar, congruent).

Vocabulary: Angles, quadrilaterals, triangles, circles, solids, coordinate planes, lines, segments, rays, planes, and space.

Euclid’s Axioms:

  • A line can be drawn from a point to any other point.
  • A finite line can be extended indefinitely.
  • A circle can be drawn, given a center and a radius.
  • All right angles are ninety degrees.
  • If a line intersects two other lines such that the sum of the interior angles on one side of the intersecting line is less than the sum of two right angles, then the lines meet on that side and not on the other side.

Familiarizing yourself with Geometry-specific concepts will help Geometry feel less like a foreign language and help you more easily decode geometric problems.

In addition, review Algebra-specific concepts, such as the properties of real numbers for addition and multiplication (commutative, associative, distributive, identity, and inverse). Recognize that you have learned and applied these properties, and you will be expected to learn and apply definitions in Geometry the same way.

Get comfortable drawing and labeling information on figures. To decode complex geometric problems, you need to organize the presented information. Correctly labeling the information will help you more easily proceed to find a solution. Apply your learnings from Algebra and practice graphing relations and functions.

Practice properly applying and evaluating formulas. Refresh your Algebra skills and make sure you are comfortable substituting values into formulas and solving for unknowns.

Recognize all of the components of a Geometry problem/proof. Although a geometric problem may be given in terms of a visual, you should practice dissecting the information and restate the problem in a more familiar structure. Consider all information to be useful information. The practice of proofs may be a new and foreign terrain in your math career, so develop a game plan to follow when organizing proofs. As you follow this plan, you’ll be more confident in your results.

  1.  Write down the given information and understand what is asked of you.
  2. Draw a picture and label it.
  3. Write any relevant statements.
  4. Substitute measures, as appropriate, to make sense of what is needed. Begin with an informal, paragraph-style proof. Informally state in words what you have, the steps to prove, and the conclusion to reach. From here, you can formalize your proof. Follow a logical order when processing your proof.
  5. Develop reasons for every statement. Consider any definitions, postulates, properties, and proven theorems that might be useful.
  6. Clean up your proof: use appropriate symbols and abbreviations.
  7. Check your logic and ensure you have used all the “givens.”
  8. If you get stuck, work backward. You will be surprised to find that writing down one idea will quickly lead to another, and soon enough, you will complete the proof!

You might find it helpful to practice algebraic proofs well before you move on to geometric proofs. Keep in mind that success in a Geometry course relies on the ability of “mature, logical thinking.”

Take it one step at a time. Patience is key. You may need extra support initially, but with practice, you will train your mind to know where to start and which path to take to get to the answer.

We know it can be daunting, but firmly believe that anyone can learn and can master math — including Geometry! Trust your abilities, use these guidelines, and before you know it, you’ll be an expert too. Enjoy the “puzzle” process. And if you ever feel like you need additional support, send us an email or give us a call: 619-224-6284, pointloma@mathnasium.com. Good luck!

Readers: Do YOU have a math-related question you’d like our education team to answer? Submit it at: //bit.ly/AskMathnasiumEducation.

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