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Goal: to use inequalities involving angles and sides of triangles Activities: 1.Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. 2.View Lesson 5-5 Powerpoint and take notes.Lesson Work through the following links 1.Khan AcademyKhan Academy 2.Rags to RichesRags to Riches 3.QuiaQuia 4.Visual RepresentationVisual Representation 4.Summary: In your notes, explain the three concepts explored in class today relating measures of sides and angles in triangles.
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Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side
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Inequalities in One Triangle Note that there is only one situation that you can have a triangle; when the sum of two sides of the triangle are greater than the third. They have to be able to reach!!
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Triangle Inequality Theorem AB + BC > AC A B C AB + AC > BC AC + BC > AB
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Triangle Inequality Theorem A B C Biggest Side Opposite Biggest Angle Medium Side Opposite Medium Angle Smallest Side Opposite Smallest Angle 3 5 m
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Triangle Inequality Theorem Converse is true also Biggest Angle Opposite _____________ Medium Angle Opposite ______________ Smallest Angle Opposite _______________ B C A Angle A > Angle B > Angle C So CB >AC > AB
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Example: List the measures of the sides of the triangle, in order of least to greatest. 10x - 10 = 180 Solving for x: Therefore, BC < AB < AC
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Using the Exterior Angle Inequality Example: Solve the inequality if AB + AC > BC x + 3 x + 2 A B C (x+3) + (x+ 2) > 3x - 2 3x - 22x + 5 > 3x - 2 x < 7
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Example: Determine if the following lengths are legs of triangles A)4, 9, ? 9 9 > 9 We choose the smallest two of the three sides and add them together. Comparing the sum to the third side: B) 9, 5, 5 Since the sum is not greater than the third side, this is not a triangle ? 9 10 > 9 Since the sum is greater than the third side, this is a triangle
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Example: a triangle has side lengths of 6 and 12; what are the possible lengths of the third side? 6 12 X = ? = – 6 = 6 Therefore: 6 < X < 18 Return to Homepage
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