1. Chapter 4-3 Inequalities in One Triangle Inequalities in Two Triangles

2. More Exciting Theorems!!  Unequal Side Theorem If two sides of a triangle are unequal in length, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side.

3. Examples for 6.9  1. In triangle ABC where AB=15 BC=10 CA=8 Identify the largest and smallest angles.

4. Examples for 6.9  1. In triangle ABC where AB=14 BC=14 CA=16 Identify the largest and smallest angles.

5. More Exciting Theorems!!  Unequal Angles Theorem If two angles of a triangle are unequal in measure, then the length of the side opposite the larger angle is greater than the length of the side opposite the smaller angle.

6. Examples  2. In triangle KMS where <K=47 o <M=51 o Identify the longest and shortest sides.

7. Examples  2. In triangle KMS where <K=65 o <M=33 o Identify the longest and shortest sides.

8. More Exciting Theorems!!  Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

9. Example  3. Identify which of the following sets of numbers could create a triangle (add the two smaller sides) sum 2 sides > longest side a. 8.6, 3.8, 4.4 b. 7.2, 5.1, 4.6 c. 3.4, 5.2, 8.6 d. 9.4, 5.9, 3.6

10. Example  4. Using Pythagorean, determine the type of triangle each set of side lengths would create. a. 4, 8, 9 b. 6, 8, 10 c. 6, 13, 19 d. 3, 3, 3

11. Example for 6.10 Determine the relationship between sides BC and EF in each case. A B C DE F a. m<A = 55 o m<D=73 o b. m<A = 43 o m<D=88 o c. m<A = 125 o m<D=62 o

12. Example Determine the relationship between <A and <D in each case. A B C DE F a. BC = 10 EF = 12 b. BC = 9 EF = 5 c. BC = 13 EF = 13