The document discusses the triangle inequality theorem which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. It provides examples of using the triangle inequality to determine the possible length of the third side of a triangle given the lengths of two sides. Specifically, it shows how to set up inequalities and determine the range of possible values for the third side.

2. How Triangle Inequality Works

4. Problem#1 The lenghts of two sides are 6 and 3. The length of the three side may be: To solve this question first you have to follow this easy steps: Step1: Add 6 and 3 which gives you 9 and 9 would be the higher range 6 3 x Step 2: Then you subtract 6 and 3 which gives you 3, 3 would be the lower range Step 3: Write an inequality with x Step 4Add the lower and higher range to the inequality **So then the inequality would be 9<x<3** The possible answer for x could be between 3 and 6 Credit-Erika Zumba

6. Problem #3 The direct distance between city A and city B is 200 miles. The direct distance between city B and city C is 300 miles. Which could be the direct distance between city C and city A . So lets analyze the question: They are saying that between A and B is 200 miles. And they are also saying that between B and C is 300 miles. They want to know that what could be the distance between A and C. A B C 300 miles 200 miles First add 200 miles and 300 miles and you get 500 miles, 50 would be the higher range Then subtract 300 miles with 200 miles and you get 100, 100 would be the lower range After that, write an inequality with x, because x is the distance between A and C Then add the 100 in the left side of the x and the 500 to the right of the x Mutiple Choice 1) 50 miles 2) 350 miles 3) 550 miles 4) 650 miles The inequality would like this 100<x<500 The possible answer could be between 100 and 500 So now look at the possible answers one of them is 50 miles but that the less than 100.The other choice is 550 miles but that answer is greater than 500, and so is 650. So that only leaves us with 350 being the answer. Answer:350 miles x Credit-Ms.Mui

7. Useful Links http://regentsprep.org/Regents/math/geometry/GP7/LTriIneq.htm http://www.mathopenref.com/triangleinequality.html