Indirect Proof and Inequalities in One Triangle

Question 1

What is an Indirect Proof?

Answer 1

A proof by contradiction, the conclusion is assumed to be false.

Question 2

What is the Triangle Inequality Theorem?

Answer 2

The sum of any two side lengths of a triangle is greater than the third side length.

Question 3

What are the steps of writing an Indirect Proof?

Answer 3

1. Identify conjecture to be proven.
2. Assume the opposite (the negation) of the conclusion is true.
3. Use direct reasoning to show that the assumption leads to a contradiction.
4. Conclude that since the assumption is false, the original conjecture must be true.

Question 4

What is the Triangle Side Length Theorem?

Answer 4

If two angles of a triangle are not congruent, then the longer side is opposite the larger angle.