Inequalities and Indirect Proof
Inequalities and Indirect Proof
Objectives:
1. Apply properties of inequality to positive numbers, lengths of segments, and measures of angles
2. State the contrapositive and inverse of an if-then statement
3. Draw correct conclusions from given statements.
4. Use indirect proofs to come to a conclusion.
6-1 Inequalities
Some Properties of Inequality
If a > b and c ( d, then a + c > b + d
Pg 205 (3, 4, 13)
If a > b and c > 0, then ac > bc and [pic]
Pg 205 (1 & 2)
If a > b and c < 0, then ac < bc and [pic]
transitive property of inequality.
If a > b, and b > c, then a > c
Pg 205 (9 & 10)
Parts are always smaller than the whole
(this is normally used for segments and angles)
If a = b + c and c > 0, then a > b
Pg 205 (12)
Theorem 6-1 The Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle
This stems from the last property of inequality
Pg 205 (5-8, 14, 15)
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