5 5 INEQUALITIES IN TRIANGLES Goal to use

Triangle Inequality Theorem The sum of the lengths of any two sides of a

Inequalities in One Triangle ¬They have to be able to reach!! 3 2 4

Triangle Inequality Theorem A ¬AB + AC > BC ¬AB + BC > AC

Triangle Inequality Theorem ¬Biggest Side Opposite Biggest Angle A ¬Medium Side Opposite Medium Angle

Triangle Inequality Theorem ¬Converse is true also ¬Biggest Angle Opposite _______ ¬Medium Angle Opposite

Example: List the measures of the sides of the triangle, in order of least

Using the Exterior Angle Inequality ¬Example: Solve the inequality if AB + AC >

Example: Determine if the following lengths are legs of triangles A) 4, 9, 5

Example: a triangle has side lengths of 6 and 12; what are the possible

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5 -5 INEQUALITIES IN TRIANGLES 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. 3. Work through the following links 1. Khan Academy 2. Rags to Riches 3. Quia 4. Visual Representation 4. 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 3 3 6 6 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.

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

Triangle Inequality Theorem ¬Biggest Side Opposite Biggest Angle A ¬Medium Side Opposite Medium Angle ¬Smallest Side Opposite 5 Smallest Angle 3 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 ________ A 65 30 C Angle A > Angle B > Angle C So CB >AC > AB B

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

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

Example: Determine if the following lengths are legs of triangles A) 4, 9, 5 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 5+5 ? 9 9>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 X=? 12 + 6 = 18 12 – 6 = 6 Therefore: 6 < X < 18 Return to Homepage