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The aim of this article is to provide information about two different types of triangles. Triangles are among the simplest geometric shapes, but they are also among the most useful. Every day, triangles shape our world in one form or another. They're present in every home and building you visit, after all it's hard to miss their distinctive triangular roof tiles that top everything from your garage to the Empire State Building! This article will help you learn about two different kinds of triangle. The first type is an equilateral triangle which has three equal side lengths. The second type is called a right triangle which has one right angle with a shorter base length than its longer height. First, let’s start off with the most obvious of the equilateral triangle’s attributes, which is that all three sides are equal. We can see that this triangle has two equal legs and an equal base. This equality of length is given one of the most famous names in all of geometry: the “side-side-side” (SSS) axiom. The SSS axiom states that if two lines are drawn with the same length, then they will make congruent angles with each other. Utilizing this information about triangles enables us to determine several integral relationships between its three different parts. For example, the law of cosines gives us a formula for finding the length of each side of any triangle, provided we know the lengths of two other sides. If we let: Then: We can see that our familiar equation for a right triangle (“A” is the length of the hypotenuse which is opposite the right angle and “B” and "C" are the other two sides). Another helpful relationship is Heron's formula which allows us to find all three sides of a triangle when one side and two angles are known. The formula is very similar to the SSS axiom, except that we use [x] [y] [z] instead of [a] [b] [c]. Now let's consider a right triangle with a few more attributes. First, it must have a hypotenuse length equal to its short side. In this case, the formula for finding the length of the hypotenuse (or "C") has changed from: To: We can see that we've added an extra variable (let's call it "D") and we've changed the SSS axiom into three separate equations for "B", "C", and "D". These equations will give us the lengths of all three sides of this special triangle. Let's talk about the Pythagorean theorem, which is one of the most well-known and useful right triangles relationships. This theorem states that: "In a right triangle, the square of the hypotenuse (a side opposite an acute angle) equals the sum of squares of other sides." Besides its use in proving that famous 22 + 42 = 52 equation, we can also use the Pythagorean theorem to find unknown values in a right triangle. This is called "solving" a right triangle and it involves rearranging one or more side lengths into equalities with each other. cfa1e77820
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