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5-5 Inequalities in Triangles

5-5 Inequalities in Triangles. Activities: Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. View Lesson 5-5 Powerpoint and take notes. Work through the following links Khan Academy Rags to Riches Quia Visual Representation

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5-5 Inequalities in Triangles

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  1. 5-5 Inequalities in Triangles • Activities: • Open GSP 4.06 and complete all steps and answer all questions for GSP Triangle Inequality Activity. • View Lesson 5-5 Powerpoint and take notes. • Work through the following links • Khan Academy • Rags to Riches • Quia • Visual Representation • Summary: In your notes, explain the three concepts explored in class today relating measures of sides and angles in triangles. Goal: to use inequalities involving angles and sides of triangles

  2. Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side

  3. Inequalities in One Triangle • They have to be able to reach!! 3 2 4 3 6 6 3 3 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. 6

  4. Triangle Inequality Theorem • AB + BC > AC A • AB + AC > BC • AC + BC > AB B C

  5. Triangle Inequality Theorem • Biggest Side Opposite Biggest Angle • Medium Side Opposite Medium Angle • Smallest Side Opposite Smallest Angle A 3 5 B C m<B is greater than m<C

  6. A 65 30 B C Triangle Inequality Theorem • Converse is true also • Biggest Angle Opposite _____________ • Medium Angle Opposite ______________ • Smallest Angle Opposite _______________ Angle A > Angle B > Angle C So CB >AC > AB

  7. Example: List the measures of the sides of the triangle, in order of least to greatest. <B = 4x <A = 2x + 1 <C = 4x -11 Solving for x: 2x +1 + 4x + 4x - 11 =180 Note: Picture is not to scale 10x - 10 = 180 Plugging back into our Angles: <A = 39o; <B = 76; <C = 65 10x = 190 X = 19 Therefore, BC < AB < AC

  8. Using the Exterior Angle Inequality • Example: Solve the inequality if AB + AC > BC C (x+3) + (x+ 2) > 3x - 2 x + 3 2x + 5 > 3x - 2 3x - 2 A x < 7 x + 2 B

  9. Example: Determine if the following lengths are legs of triangles B) 9, 5, 5 A) 4, 9, 5 We choose the smallest two of the three sides and add them together. Comparing the sum to the third side: 4 + 5 ? 9 9 > 9 5 + 5 ? 9 10 > 9 Since the sum is not greater than the third side, this is not a triangle Since the sum is greater than the third side, this is a triangle

  10. 12 6 X = ? Example: a triangle has side lengths of 6 and 12; what are the possible lengths of the third side? 12 + 6 = 18 12 – 6 = 6 Therefore: 6 < X < 18 Return to Homepage

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