Triangle Inequality Theorem
Look at the construction below. Can you move the points in the construction so that segments a, b, and c form a triangle? To form a triangle all points should match up perfectly.
In this exploration, you will determine the conditions required for side lengths to form triangles. This set of conditions is known as the Triangle Inequality Theorem.
Answer the following questions below. Use the construction above to help you if you want.
1) Set the side lengths a, b, and c to 7, 10, and 19, respectively. Can these three segments form a triangle? What is the sum of the two shortest lengths and how does it compare to the longest length?
2) Set the side lengths a, b, and c to 3, 4, and 5, respectively. Can these three segments form a triangle? What is the sum of the two shortest lengths and how does it compare to the longest length?
3) What has to be true about the relationships between the sides in order to be able to form triangles? Use the sentence STEM to guide your thinking: " To form a triangle the sum of the ______________________________ must be ____________________ the longest side.
Without using the construction above can the side lengths 5, 8, 12 form a triangle?
Without using the construction above can the side lengths 1, 3, 4 form a triangle?
Without using the construction above can the side lengths 5,11, 14 form a triangle?