34.	+Triangle+Inequality+Theorem

= = = = = = = = =__**//By: Alec Schwartz//**__ //__Triangle Inequality Theorem__//= The triangle inequality theorem is used when you are looking to find the longest or shortest side length. Also it is used when looking to put sides or angles in order from least to greatest, and when you are looking to find the possible third side length. You can also use it to see if a triangle can be formed by the three lengths.
 * Summary**

least to greatest(angles):** 1) you have to find the smallest, longest, and the middle side length. 2) then you have to see which side lengths are across from which angles. 3) when you do this you will find that the smallest angle is right across from the smallest side, and the largest side is right across from the largest angle. The middle side length will be across from the angle in the middle of the least to greatest. (EX:1)
 * Rules

1) you have to find which angle measure is the greatest out of the three given ones. 2) then when you do this, you will know that the longest angle is straight across from the longest side. (EX:2)
 * longest side length:**

1) to find this you have to add and subtract the two side lengths the gave you. 2) after you have done this then you will have to say the possible third length is less than the two side lengths added together, but its more than the two side lenghs subtracted together. (EX: 3)
 * possible length of third side:**

when doing the triangle inequality theorem there are some certain things to follow. For example: when you are solving for the possible length of the third side, you have to write it like this- 2/5<y<22/15. when observing and looking to see if a triangle can be formed by the three sides given you have to add up the two smaller sides and check if they are greater than the largest side. If so a triangle can be formed, it cant be formed if smaller than larger side or equal to it.
 * properties/formulas**


 * A key aspect when doing the triangle inequality theorem to find order from least to greatest or to find the largest/smallest side is to always match up the smallest side length to the smallest angle length, and the middle side length to the middle angle length, and the largest side length to the largest angle length.***
 * The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides.(http://www.mathopenref.com/triangleinequality.html)

useful websites!-- 1) [|Finding the possible third side] 2) [|Can a triangle be formed with the following measures?] 3)[|Is it possible to have a triangle with these side lengths?]