Geometry is a fascinating subject that children as well as adults can appreciate.

It can probably go without saying that a lot of 10th graders wouldn't be interested in geometry if it wasn't required of them for school. After all, math is hard and boring. It doesn't have to be, though. For example, a lot of people think geometry can be very interesting and a lot of fun. There are some facts about geometry that you might find interesting, or at the very least some information that may help you in your next geometry class.

## The Angles of a Triangle

Triangles are some of the most elementary shapes to be discussed in geometry. Many beginning geometry lessons begin with them, and even non-students can recognize a triangle if they see one. A triangle is a shape with three sides and three angles. That much is known almost universally, but one thing that isn't as well known is the fact that all three angles of a triangle add up to 180 degrees. No matter how big a triangle is or how oddly it may be shaped, all three angles will always add up to 180 degrees. Naturally, this makes finding an unknown angle of a triangle much easier as long as you know the measurements of the other two angles. Just take the sum of the two known angles and subtract it from 180.

## The Pythagorean Theorem

Learning the measurement of one side of a triangle isn't as easy as finding out its angles, but there is still an easy formula that you can use for that problem. It's called the Pythagorean Theorem, and it basically means that the squares of the triangle's legs add up to the square of the hypotenuse, or the longest side of the triangle. It is usually written as a2 + b2 = c2, with a and b representing the legs and c representing the hypotenuse. Just plug the numbers into the equation and you should be able to find the length of any side of the triangle -- a calculator helps a lot here.

## The Banach-Tarksi Paradox

One of the strangest theorems in geometry is the Banach-Tarski paradox. Essentially, this theorem states that a sphere can be divided into six equal parts that can then be reassembled into two spheres of the same size. The pieces can in fact be reassembled into any object of any shape and size. This shouldn't be possible, which is why it is a paradox, and the shape of the pieces tends to challenge one's understanding of volume and area.

## Euclidean Geometry

Euclidean geometry is one of the earliest forms of geometry, and many of its principles are still in use today. It was developed by the mathematician Euclid, who lived around 300 B.C. It is primarily based around five main axioms: any two points can be connected by a straight line, any straight line segment can be stretched infinitely, a circle can always be created by any line segment by having one point at the center and the segment as the circle's radius, all right angles are identical, and two lines that intersect with a third line will later intersect with each other if the sum of the inner angles formed by the first intersection is less than two right angles.

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