### Start Learning Now

Our free lessons will get you started (Flash® 10 required).

### Indirect Proofs and Inequalities

• The three steps to writing an indirect proof:
• Assume that the conclusion is false
• Show that the assumption leads to a contradiction of the hypothesis or something you know is true, like some fact or theorem
• Point out that the assumption must be false, and, therefore, the conclusion must be true
• Inequality: For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c
• Properties of Inequality:
• Comparison Property: a > b, a < b, a = b
• Transitive Property: If a < b and b < c, then a < c
• Addition and Subtraction Properties: If a > b, then a + c > b + c, and a – c > b – c
• Multiplication and Division Properties: If a > b, then ac > bc, and a/c > b/c
• Exterior Angle Inequality Theorem: If an angle is an exterior angle of a triangle, then its measure is greater than the measures of either of its remote interior angles

## Indirect Proofs and Inequalities

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.