5-5 Inequalities in Triangles

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Presentation transcript:

5-5 Inequalities in Triangles Goal: to use inequalities involving angles and sides of 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 Visual Representation Summary: In your notes, explain the three concepts explored in class today relating measures of sides and angles in triangles.

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

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

Triangle Inequality Theorem AB + AC > BC AB + BC > AC AC + BC > AB B C

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

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

<A = 39o; <B = 76; <C = 65 Example: List the measures of the sides of the triangle, in order of least to greatest. <A = 2x + 1 <B = 4x <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

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

Example: Determine if the following lengths are legs of triangles B) 9, 5, 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

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