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Geometry Notes – Lesson 5.5 Name _______________________________ Comparison Property of Inequality. If a = b + c and c> 0, then _________ Corollary to the Triangle Exterior Angle Theorem. The measure of an exterior angle of a triangle is __________________ than the measure of each of its remote interior angles. __________ > __________ and _________ > _____________ Example: In the diagram to the left, BC || DE. Why is m4 m3 ? 1. m4 m2 by ______________________ 2. m2 m3 by _______________________ 3. m4 m3 by _______________________ Theorem 5-10. If two sides of a triangle are not congruent, then the larger _____________ lies opposite the longer ___________. If XZ > XY , then mY m __________ Examples: List the angles of the triangle in order from smallest to largest. 1. 3. PO 2. = 38, RO = 26, PR = 28 Theorem 5-11. If two angles of a triangle are not congruent, then the longer ___________ lies opposite the larger ______________. If mA mB , then BC > ________ Examples: List the sides in order from shortest to longest 4. 5. 6. Theorem 5-12 Triangle Inequality Theorem. The sum of the lengths of any 2 sides of a triangle is __________ than the length of the ___________ side. XY + YZ > ________ and YZ + ZX > _________ and ZX + XY > __________ Example: Can a triangle have sides with the given lengths? 4. 4m, 7m, and 8m 5. 6m, 10m, and 17m 6. 2.5m, 3.5m, and 6m Example: If a triangle has two sides with lengths as given, Describe possible lengths of the third side. 7. 4in., 7 in. 8. 11m, 20m 9. 24in., 37in.