 Earlier in this chapter, we looked at properties of individual triangles using inequalities.  We know that the largest angle is opposite the longest.

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Presentation transcript:

 Earlier in this chapter, we looked at properties of individual triangles using inequalities.  We know that the largest angle is opposite the longest side.  Also, the smallest angle is opposite the shortest side.

 We have studied several ways to show that 2 triangles are congruent.  SSS, SAS, ASA, HL and AAS are the Theorems that we can use to prove one triangle congruent to a second triangle.

 The SAS Theorem told us that if 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent.

 The Hinge (SAS Inequality) Theorem states: If two sides of one triangle are congruent to two sides of another triangle, the triangle with the larger included angle will have a larger third side.

 Given,  Then BC > YZ 2 A B C 1 X Y Z

 The Converse of the Hinge Theorem states: If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the triangle with the larger third side will have a larger included angle.

 Given BC > YZ,  Then 2 1 A B C X Y Z

R  60>5x-20  80>5x  16>x or x<16 UT S ° (5x-20)°

 p.336 #1-2, 6-14 all  Proof #15  P.339 #26-27