5-2 Inequalities and Triangles Definition of 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

Review of the Symbols = Not equal to > Greater than or equal to < Less than or equal to > Not greater than or equal to < Not less than or equal to

Review of the Properties Comparison Property: a < b, a = b, or a > b Transitive Property: If a < b and b < c, then a < c 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 If a < b, then a + c < b + c, and a – c < b – c Multiplication and Division Properties If c > 0, and a < b, then ac < bc and a/c < b/c If c > 0, and a > b, then ac > bc and a/c > b/c If c < 0, and a < b, then ac > bc and a/c > b/c If c < 0, and a > b, then ac < bc and a/c < bc

Exterior Angle Review Exterior angle – forms a linear pair with one of the angles of a triangle. Example: 2 &6… 2 & 5 Remote interior angles – the two angles that do NOT form a linear pair with the exterior angle. Example: 5 with 1 & 3 6 2 5 7 3 8 1 4 9

Theorem 5.8 82° 1 3 2 Exterior Angle Inequality Theorem – If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles. Name two angles in ΔCDE that have a measure less than 82°. 2 and 3 Try #2 Check your Progress on page 282 5 and 6

Theorem 5.9 If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. Greater Measure Longer Side

Theorem 5.10 If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. Greater Measure Longer Side

Try these – page 284 #1-9 Homework #32 P. 285 11-16, 18-36 (x 3’s), 40-42, 50, 52