Course: Applied Geometry Aim: What is Triangle Inequality Theorem Aim: What is Triangle Inequality? Do Now: Sketch 9

Course: Applied Geometry Aim: What is Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Y ZX XY + YZ > XZ YZ + XZ > XY XZ + XY > YZ

Course: Applied Geometry Aim: What is Triangle Inequality Theorem The length of the third side must be somewhere in between the SUM and the DIFFERENCE of the lengths of the first two sides. Y ZX XY – YZ < XZ < YZ + XY

Course: Applied Geometry Aim: What is Triangle Inequality Theorem TRIANGLE FORMED? NO YES NO YES

Course: Applied Geometry Aim: What is Triangle Inequality Theorem Is it possible to form a triangle with side lengths 4 cm., 6 cm., and 10 cm.? Explain No, is not > 10, even though = 2 < 10 Is it possible to form a triangle with side lengths 10 cm., 8 cm., and 3.5 cm.? Explain yes, > 3.5 and = 2 < 3.5 Model Problems

Course: Applied Geometry Aim: What is Triangle Inequality Theorem The lengths of two sides of a triangle are given. Write an inequality to represent the range of values for z, the length of the third side. Model Problems 8 ft, 12 ft. 4 < z < 20 6 cm, 6 cm 0 < z < 12

Course: Applied Geometry Aim: What is Triangle Inequality Theorem 5 7 CB A 9  A,  B, OR  C? Which is the largest angle of  ABC? Which is the smallest? AA CC If one side of a triangle is greater in measure than a second side, then the angle opposite the first side is greater in measure than the angle opposite the second side. If BC > AC, then m  A > m  B. If m  A > m  B, then BC > AC. Also true Model Problems

Course: Applied Geometry Aim: What is Triangle Inequality Theorem In a triangle, the angle with the smallest measure is opposite the shortest side of the triangle. The angle with the greatest measure is opposite the longest side of the triangle. Y ZX m  ___ < m  ___ < m  ___ Fill in the blanks Segments: Angles: ___ < ___ < ___ Conjecture: ZXY x z y zxy Who’s Bigger?

Course: Applied Geometry Aim: What is Triangle Inequality Theorem Who’s Bigger? List the angles of each triangle in order from smallest to largest.  B <  C <  A  S <  T <  R

Course: Applied Geometry Aim: What is Triangle Inequality Theorem Model Problems List the sides of each triangle in order from shortest to longest. HJ < JK < HK 60 o BC < AC < AB 45 o 75 o

Course: Applied Geometry Aim: What is Triangle Inequality Theorem A triangle has sides measuring 3, 5, and 7. Is it a right triangle? If not what type? The Pythagorean Theorem, a 2 + b 2 = c 2 will show us if it’s a right triangle. 7 would be the measure of the hypotenuse = 7 2  = 49 Not a right  ? a 2 + b 2 < c 2 a 2 + b 2 > c 2 Obtuse  Acute  a = 3, b = 5, c = = 7 2  34 < 49 Obtuse or acute? What Type of Triangle?

Course: Applied Geometry Aim: What is Triangle Inequality Theorem The numbers represent the length of the sides of a triangle. Classify each as acute, obtuse, or right. What Type of Triangle? 13, 84, 85 a 2 + b 2 < c 2 a 2 + b 2 > c 2 Obtuse  Acute  = = = 7225 rt. triangle 6, 11, = = < 196 obtuse triangle = > 16 acute triangle