5.2.1 Indirect Proof and Inequalities in One Triangle

Question 1

indirect proof

Answer 1

or proof by contradiction, the conclusion is assumed to be false

Question 2

Theorem

Answer 2

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

Question 3

Theorem

Answer 3

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

Question 4

Triangle Inequality Theorem

Answer 4

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

Question 5

Writing an Indirect Proof

Answer 5

1. Identify the conjecture to be proven.
2. Assume the opposite (the negative) 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.