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Honors Geometry Name: ________________________ 6.4 Class Notes Date: ___________________Pd:___ Inequalities in Triangles Warm Up: 1. Prove Directly: If x and z are multiples of y, then x+z is a multiple of y. 2. Given: Points R, S, T and W; RS and TW are skew Prove: RT and SW are skew Theorem 6.2: If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side. R Z 3 T 1 2 S Theorem 6.3: If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. R T S Corollary 1: The perpendicular segment from a point to a line is the shortest segment from the point to the line. Corollary 2: The perpendicular segment from a point to a plane is the shortest segment from the point to the plane. Theorem 6.4 - The Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. C A B Z Example 1) The length of two sides of a triangle are 3 and 5. The length of the third side must be… Homework: p. 222 #1-12 all p.223 #13-20 all