Inequalities in Two Triangles

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Inequalities in Two Triangles Topic 5-8 Inequalities in Two Triangles

Hinge Theorem (SAS Inequality Theorem) If two sides of one triangle are congruent two two sides of another triangle, and the included angles are not congruent, then the longest side is opposite the larger included angle. mDBC > mDBA Then DC > AD

Examples - Which side is longer?

Converse of the Hinge Theorem (SSS Inequality) If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side. If BC > EF Then mA > m D

Example Find the range of possible values for x Upper limit mCDF < mEDF 3x-15 < 66 3x < 81 x < 27 Lower limit mEDF > 0 3x-15 > 0 3x > 15 x > 5 5 < x < 27

Example Find the range of possible values for x Upper limit: mCAD < BAD 2x - 16 < 36 2x < 52 x < 26 Lower limit: mCAD > 0 2x – 16 > 0 2x > 16 x > 8 B C D 8 < x < 26