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Section 5.5 Notes – Geometry Inequalities in Triangles Name: _____________________________ Period: _________ Goal: Be able to use inequalities involving angles of triangles and sides of triangles. Theorem: The _____________ side of a triangle is opposite the ______________ ____________. Theorem: The _____________ angle of a triangle is opposite the _____________ ____________. Directions: List the angles or sides of each triangle in order from smallest to largest. 1. 2. Directions: Determine which segment is shortest. 3. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is ______________ than the length of the 3rd side. Directions: Can a triangle have sides with the given lengths? Explain. 4. 5. 18, 32, 21 Directions: The lengths of two sides are given. Describe the lengths for the possible third side. 6. 5 and 11 7. 21 and 27 8. List sides in order from shortest to longest in ABC if mA 10x, mB 5x 17, and mC 7x 1 9. List angles in order from shortest to longest in ABC if AB 3x 18, BC 5x 3, and AC 7x 12 when the perimeter is 108. Exterior Angle Inequality Theorem The measure of an exterior angle is _______________ than the measure of each of its remote interior angles. 10. Find m1 Recap: 11a. Explain why m4 m1. 11. 11b. Explain why m3 m1. 11c. Use ABC to describe the possible lengths of AC . 12. Can a triangle have length of 2, 3, and 6? 13. In XYZ, XY 5, YZ 8, XZ 7 . Which angle is the largest? 14. In PQT, mP 50 and mT 70 . Which side is the shortest? Directions: List the side lengths in order from longest to shortest of the following triangles. 15. 17. 16. If 54 and 58 are the lengths of two sides of a triangles, what are the possible lengths of the third side of the triangle? 18. What is wrong with this picture? Directions: 19. Find the measure of the indicated angles. 20.