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5.5 Inequalities of a Triangle

5.5 Inequalities of a Triangle. Goal: Compare measurements of a triangle to decide which side is longest or which angle is largest and use the Triangle Inequality. Standard 16.0.

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5.5 Inequalities of a Triangle

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  1. 5.5 Inequalities of a Triangle Goal: Compare measurements of a triangle to decide which side is longest or which angle is largest and use the Triangle Inequality

  2. Standard 16.0 • Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. • Los estudiantes realizan construcciones básicas con una regla y un compás, tales como la bisectriz de un ángulo, las bisectrices de los segmentos perpendiculares, y la línea paralela a una línea dada a través de un punto afuera de la línea.

  3. Theorem 5.10 B If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. A C AC > AB mB > mC

  4. Theorem 5.11 B If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. A C mB > mC AC > AB

  5. Theorem 5.12 Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. B 1 A C m1 > mA and m1 > mB

  6. Theorem 5.13 Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B A C AB + BC > AC AB + AC > BC BC + AC > AB

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