Parallel Lines        Congruent Tri.        Congruent R. Tri.        Isosc. and Equil.        Quadrilaterals        Parallelograms        Ratios        Similar Polygons        Special Triangles       Circles        Area        Coordinate Geo.    Triangle Ineq.        Solids        Computer Fun

On this page we hope to clear up any problems that you might have with triangle inequality.  Scroll down or click any of the links below to start understanding triangle inequality better! Triangle Inequality Theorem Inequalities for two triangles Quiz on Triangle Inequality Triangle Inequality Theorem The sum of the measures of any two sides of any triangle is greater than the measure of the third side. In English, that means that in a triangle, you can pick any two sides' measures, and when you add them together, the sum will be greater than the measure of the third side. 1. Problem: Can a triangle have the following measures? 3, 10, and 8 9, 17, and 8 Solution: The first set of measures can form a triangle because 3 + 10 is greater than 8 8 + 10 is greater than 3 and 3 + 8 is greater than 10. The second set of measures cannot form a triangle because 9 + 8 is equal to 17. Back to Top  The two theorems that apply to inequalities in two triangles are explained below (and illustrated in the figure below). 1.  If two triangles have two sides that are congruent, the triangle with the larger third side will have a larger included angle. 2.  If two triangles have two sides that are congruent, the triangle with the larger included angle will have a larger third side. Back to Top  Take the Quiz on triangle inequality.  (Very useful to review or to see if you've really got this topic down.)  Do it!