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 Triangle Side Inequalities The sum of the lengths of any two sides of a triangle is greater than the length of the third side. 1) AB + BC > AC 2) AB + AC > BC 3) AC + BC > AB Notice in the figure that as vertex C moves closer and closer to side AB, the sum of the lengths of sides AC and CB gets smaller. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Can it ever reach the point where AC+CB=AB? Yes, but then it is no longer a triangle. It would be a straight line!. If AC + CB is not greater than AB, then the sides are not longer enough to make a triangle. Is a triangle with these three sides possible? a. 12, 13, 21 b. 7, 8, 15 Solution: a. 25>21. Yes. b. 15 = 15. No. A triangle has two sides of length 4cm and 12 cm. Describe the possible length of the third side, x. Solution: There are several possibilities: But all of them must verify the triangle side inequalities: x+4>12, then x>8 x+12>4, then x>-8 4+12>x, then 16>x Consequently 16 > x > 8