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

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Presentation transcript:

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

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.

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

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

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.

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

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

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.

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

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

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

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