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What Is Geometry?

Geometry is a well-known branch of mathematics. Specifically, geometry involves the study of sizes, shapes, angles, and dimensions of objects. Circles, triangles, squares, and rectangles are all studied via flat geometry. Three-dimensional objects such as cubes, spheres, and cones are studied in solid geometry. Geometry involves the study of angles, the lengths of sides, area, volume, and much more.

There are a number of different concepts that are studied with geometry. To start, the most basic concepts include points, lines, planes, and solids. Things get more complex when we look at more complicated shapes, such as triangles, quadrilaterals, trapezoids, polygons, circles, parallelograms, etc. With geometry, students also learn the basics of measuring perimeter and area of shapes, as well as angles and congruent shapes.

Geometry has many different applications in real life. In fact, most people use geometry daily in some capacity. To start, many architects will use computer-aided design (CAD) programs to design blueprints for new constructions. Geometry can also be used in the design of factory systems in manufacturing plants, video game productions, and virtual reality construction. Geometry is also very important when it comes to things like astronomy, cartography, and even robotics.

Subdisciplines of Geometry

  • Plane or flat geometry
  • Solid geometry
  • Spherical geometry
  • Euclidean geometry
  • Analytic geometry
  • Projective geometry
  • Differential geometry
  • Non-euclidean geometries
geometry sphere cube cylinder

How to Approach Learning Geometry

Geometry is actually not that difficult to grasp, as long as you understand the basic formulas needed to calculate things like perimeter, area, radius, diameter, etc.

Before you jump into geometry, make sure that you are refreshed on elementary mathematics. We recommend studying PEMDAS and brushing up on elementary algebra before jumping into geometry. Just as well, it will be helpful to have a graphing calculator on hand while learning the more complex geometric concepts. This will make a huge difference when you get into concepts like quadrilaterals, dissections, etc.

We also recommend learning the Pythagorean theorem before starting any type of geometry class, as this will put you at an advantage from the start.

Geometry Student Curriculum FAQs

The geometry that is taught in middle school is very elementary. Specifically, middle school geometry classes are used to teach students the basic fundamentals of geometry tools. Students may also learn how they can apply elementary geometric concepts to real-life scenarios. Specifically, students will study lines, line segments, congruence, angles, triangles, and quadrilaterals.

High school geometry is a bit more complex than middle school geometry, but still studies the simpler aspects of geometry. Students will be introduced to area, volume, and perimeter, as well as the formulas needed to calculate such concepts with shapes. Students will also begin to deal with calculating the circumference, diameter, and radius of a circle. Advanced high school geometry classes will dive into the Pythagorean theorem, complex quadrilaterals, dissections, and proof. High school students will be introduced to elementary trigonometric concepts as well.

Those who are entering high school or approaching college can prepare themselves for more advanced geometric classes in a few different ways. To start, it would be wise to brush up on your vocabulary. If you’re not familiar with rays, vertex, or symmetry, it may be smart to start studying these concepts ahead of time. We also recommend getting a protector to make studying a lot easier, as well as a very good mechanical pencil. Before entering college geometry, you may be required to purchase a graphic calculator or scientific calculator.

College-level geometry takes the concepts taught in middle school and high school and expands upon them. Typically, students will study both Euclidean and neutral geometric concepts, with a strong emphasis on logical arguments. Typically, introductory college geometry classes will review elementary concepts before diving into synthetic and algebraic concepts. Students will study all two-dimensional and three-dimensional shapes, the concept of congruence, synthetic Euclidean geometry, and plane geometry. Students will also likely be taught how to have better problem-solving skills to solve geometric problems faster. From there, college students will usually move on to trigonometry. Trigonometry involves many geometric concepts, but will introduce trigonometric functions, graphs, inverse functions, angle formulas, and polar coordinate systems. It’s necessary to have a solid understanding of geometry before entering into a trigonometry class.

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How Do I Become a Geometry Tutor?

If you have a passion for teaching others and love geometry, becoming a geometry tutor is easy. You need a minimum of a high school degree or GED to start teaching kindergarten and middle school grade levels. You may need a degree in a specialist subject for higher-level geometry courses depending on the level of practice you plan to teach. The costs of geometry tutors vary because you will set your pay rates and time schedules depending on your own experience and circumstances.

Your first step will be to decide which topics you’d like to tutor. Then choose the age groups and grade levels you want to teach. Learn the curriculum and critical concepts for those grade levels. And lastly, establish your teaching methods, tools, and eventually, you will create your own course materials over time as you get more experience working with students.

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