The Triangle Inequality Theorem is a theorem in mathematics that states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is very important when it comes to solving problems involving triangles, and it is something that you should definitely learn before taking your ACT exam! In this blog post, we will go over the basics of the Triangle Inequality Theorem and how to apply it to various problem scenarios.

So, what exactly is the Triangle Inequality Theorem? Put simply, it states that the sum of the lengths of any two sides of a triangle is always greater than or equal to the length of the third side. This theorem is based on the fact that triangles are geometric figures with three sides and three angles. The theorem is named after the Greek mathematician Euclid, who first proved it in his book Elements.

Now that we know what the Triangle Inequality Theorem is, let’s take a look at how to apply it to solving problems. Suppose we have a triangle with sides of lengths A, B, and C. We can use the theorem to find out whether or not this triangle is possible by checking to see if the sum of the lengths of two sides is greater than or equal to the length of the third side. For example, if we know that A + B = C, then we can immediately tell that this triangle is not possible because the sum of the lengths of two sides (A and B) is equal to the length of the third side (C).

Now let’s try a more difficult problem. Suppose we have a triangle with sides of length A, B, and C, and we want to know if it is possible for this triangle to have a perimeter of P. We can use the Triangle Inequality Theorem to solve this problem by checking to see if the sum of the lengths of any two sides is greater than or equal to P. For example, if we know that A + B >= P, then we can immediately tell that this triangle is possible because the sum of the lengths of two sides (A and B) is greater than or equal to the perimeter (P).

As you can see, the Triangle Inequality Theorem is a very useful tool for solving problems involving triangles. If you’re working on your ACT prep, make sure you brush up on this theorem so that you’ll be prepared to tackle any triangle-related questions that come your way! Thanks for reading and good luck with your exam!