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Transcript

5.5 Inequalities In One Triangle Essential Question: How do you determine the largest/smallest sides and angles in a triangle? Theorem If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. Theorem If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. Example: Write the measures in the triangle in order from least to greatest. Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. This theorem is used to determine if a triangle can be formed from a given set of side lengths (the sum of the smaller sides must be greater than the larger side). Example: Determine if it is possible to construct a triangle with the given side lengths. 1. 2. 3. 4. 3 3 9 2 cm, 4cm, 5cm in, 3in, 8in ft, 5 ft, 11 ft cm, 2cm, 2cm Determining the length of the third side of a triangle If you know two side lengths of a triangle, you may determine the possible lengths of the third side: ______ < x < _______ To find the value of the first blank: subtract the given values To find the value of the second blank: add the given values Example: Two of a triangle’s side lengths are given. Describe the possible lengths of the third side. 1. 2. 3. 10 cm, 14 cm 8 ft, 17 ft a units, b units Example: Determine the possible values of x