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## Geometry for Beginners – The Most Important Formulas in Geometry

Welcome to Geometry for Beginners. If you’ve read so many of these geometry for beginners articles, you’ve started to realize that geometry has a lot of formulas! In fact, it is the most formula-dependent subject of all math subjects. You may start to wonder if all the formulas are equally important – hoping you can skip learning some of them. My first piece of advice for you is that * the most important formulas are the ones you understand, remember and can easily use*. These formulas lead you to success, while the formulas you cannot use lead to failure. I will admit, however, that there are areas of formulas that I consider CRITICAL both for your geometry course and for your future.

To be successful in your geometry course, you must be able to understand and use all the formulas you come across. There are, however, three areas where formulas are essential because of their actual applications. You cannot afford to have gaps in your knowledge in these critical areas.

**3 most important categories of geometric formulas:**

**1) Anything about triangles.** Because the study of the triangle includes nearly all geometry, most trigonometry, and has a myriad of real-life applications, you just need **must learn everything!**

You will study the Pythagorean theorem and the Pythagorean triples which allow you to find *missing sides of right triangles*. You will learn “special cases” of right triangles – 30 to 60 right triangles and 45 right triangles – which allow you to find the missing sides and/or angles.

You will learn the meaning and usage of SOHCAHTOA (pronounced sew-cah-toe-a). It allows you to find *missing angles and/or sides of ANY right triangle*.

The law of sines and the law of cosines will allow you to do the same for *non-right triangles*.

You really need to know everything!

**2) Two-dimensional concepts of perimeter and area of polygons.** Because these formulas have so many real world applications – fencing a property, wallpapering the house, painting, landscaping, building, etc. – these formulas are extremely important. You will learn formulas for many different polygons and to test success in your classroom you must learn them all. but you need to anchor the formulas for triangles, quadrilaterals, hexagons and circles.

**3) Three-dimensional concepts of surface and volume. **Go to any grocery store to find applications of these concepts. The wrapper of a cereal box represents surface area while the cereal itself represents volume. A can of soda or soft drink represents the surface; pop represents volume. A tissue box represents a surface. Tissues represent volume.

The number of possible 3D figures is huge, so focus on those figures with common real-life applications. Of course, this includes spheres, cylinders, cones and 3, 4 or 6 sided prisms and pyramids on the base.

In summary, everything about triangles is essential and MUST be learned thoroughly. When discussing other topics, judge importance by daily application. If in doubt, ask your teacher. However, do not disregard my initial statement. **The most important formulas for you are the ones you learn and can use!**

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