5.6: Inequalities in Two Triangles and Indirect Proof

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5.6: Inequalities in Two Triangles and Indirect Proof GEOMETRY: Chapter 5 5.6: Inequalities in Two Triangles and Indirect Proof

Theorem 5.14: Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 335.

Theorem 5.15: Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 335.

Ex.1 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 336.

Ex.2 Two runners start together and run in opposite directions. Each one goes 1.5 miles, changes directions, and goes 2.4 miles. The first runner starts due north and turns 100 degrees towards the east. The other runner starts dues south and turns 130 degrees towards the west. Both runners return to the starting point. Which runner ran farther? Explain. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 337.

5.6, p. 305, #7-14 all