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A triangle is a 3-sided enclosed figure, with 3 angles and 3 vertices. The sum of the measures of the angles of a triangle is 180 degrees. There are several different types of triangles, which I will introduce and explain as well as how to find the area of triangles, lengths of the sides of triangles, and measurement of the angles of triangles.

First type of triangle is the right triangle. The distinguishing characteristic of this triangle is that it has 1 right angle, or 90 degree angle. The other two angles in the triangle are acute angles, which are angles less than 90 degrees in measure. The total sum of the angles is 180 degrees. From the right triangle comes the Pythagorean theorem which is a way to find the lengths of the sides of the right triangle, given the length of 2 of the 3 sides. If the sides of the triangle are labeled "a", "b" and "c", with "c" being the hypotenuse of the right triangle (the side opposite the right angle) then "a" squared plus "b" squared equals "c" squared.

There are 2 special right triangles where the Pythagorean Theorem will not need to be used to find the lengths of the sides. Those cases are the 45-45-90 right triangle and the 30-60-90 right triangle. The 45-45-90 right triangle has 2 angles of 45 degrees each and on 90 degree angle. In this case the hypotenuse is square root of 2 times the length of one of the sides, and the other 2 sides are the same in length. If the length of the hypotenuse is given, then the length of each other side is obtained by dividing by the square root of 2.

In the 30-60-90 right triangle, there is a 30 degree angle, a 60 degree angle and a 90 degree angle. The length of the hypotenuse is twice the length of the shortest side of the triangle (side opposite the 30 degree angle) and the length of the longer side (side opposite the 60 degree angle) is the square root of 3 times the shorter side.

From a right triangle, using trigonometry you can get the lengths of the sides of the right triangle given the length of only 1 of the 3 sides. The trigonometric functions used mainly in this calculation is Sine, Cosine and Tangent. Trigonometry is a topic for another discussion though.

The isosceles triangle is a triangle with 2 sides of equal length. An isoceles triangle could be a right triangle if it is a 45-45-90 right triangle because as I mentioned previously the 45-45-90 right triangle has 2 equal length sides.

An equilateral triangle is a triangle with the lengths of all 3 sides equal. That

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