Converse of Hinge Theorem

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Presentation transcript:

Converse of Hinge Theorem If 2 sides of 1 triangle are  to 2 sides of another triangle, and the included angle of the 1st is larger than the included angle of the 2nd, then the 3rd side of the 1st is longer than the 3rd side of the 2nd. Converse of Hinge Theorem

< < < Use hinge theorem: complete with <, >, or =. m1 ____ m2 KL ____ NQ DC ____ FE < < <

The side opposite the larger angle is greater than the other side. Finding a restriction for x. Hinge theorem is applied here because the triangles have two pairs congruent sides. 10 60° 50° 2x + 6 3x + 2 The side opposite the larger angle is greater than the other side. 3x + 2 > 2x + 6 x > 4