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Inequalities in Two Triangles

Inequalities in Two Triangles. Geometry CP2 (Holt 5-6) K. Santos. Hinge Theorem (5-6-1). If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across the larger included angle. B E

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Inequalities in Two Triangles

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  1. Inequalities in Two Triangles Geometry CP2 (Holt 5-6) K. Santos

  2. Hinge Theorem (5-6-1) If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across the larger included angle. B E A C D F If m<A > m<D then BC > EF

  3. Converse of the Hinge Theorem (5-6-2) 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 across from the longer third side. H L G J K N If GH > KL then m<J > m<N

  4. Example—Comparing Sides Compare: BC and AB A B C Given: m<ADB = 64 and m<CDB = 65 9 9 D By using the Hinge Theorem BC > AB

  5. Example---Comparing angles Compare: m<EGH and m<EGF F 10 12 E G 9 12 H By the converse of the Hinge theorem m<EGF > m<EGH

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