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Transcript
INEQUALITIES IN TWO TRIANGLES Geometry CP1 (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 A If m<A > m<D then BC > EF C D F 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 If GH > KL then m<J > m<N N Example—Comparing Sides Compare: BC and AB Given: m<ADB = 64° and m<CDB = 65° A B 9 C 9 D AD = CD BD = BD By using the Hinge Theorem BC > AB m<CDB >m<ADB Example---Comparing angles Compare: m<EGH and m<EGF F 10 E 9 12 G 12 H FG = HG EG = EG EF > EH By the converse of the Hinge theorem m<EGF > m<EGH
