Triangle Inequality Theorem
Given AB=3 and AC=5, drag point C around to see what BC can be.
What is the smallest value you can get for BC?
What is the LARGEST value you can get for BC?
If "x" is the length of the third side (), write an inequality expressing the range of values for x.
If BC=2 or 8, triangle ABC is called a "degenerate triangle" (yes, really), which is why we don't typically include those values in our inequality. Describe what a degenerate triangle looks like.
Use the sliders to change the side lengths AB and AC.
What are the two new side lengths you picked?
Using your new side lengths, write an inequality expressing the possible lengths of the third side.
Summary
Two side lengths of a triangle are a and b. Let x be the length of the third side. Write an inequality expressing a range of values for x in terms of a and b. (In other words, what is the pattern that you noticed above? Can you write it generally?)