7-4 Triangle Inequality Theorem

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Presentation transcript:

7-4 Triangle Inequality Theorem The sum of the measure of any two sides of a triangle is greater than the third side. C AB + BC > AC AB + AC > BC BC + AC > AB B A

Ex. 1 Determine if the three numbers can be measures of the sides of a triangle. If no, explain. 13, 28, 19 9, 4, 4 c. 9, 7, 2 Yes, 13 + 19  28 13, 19, 28 NO, 4 + 4  9 4, 4, 9 NO, 7 + 2  9 2, 7, 9

Ex. 2 If two sides of a triangle have the following measures, find the range of possible measures of the third side. 10, 7 b. 18 , 11 18 + 11  x x + 11  18 10 + 7  x x + 7  10 29  x 17  x x  7 x < 29 x < 17 x  3 3 < x < 17 7 < x < 29

Side – Angle Inequalities If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the smaller side.

Ex. 1 Write the measurements of the angles in order from least to greatest. 52 12 B C 43 Step 1. Write the sides in order from least to greatest. AB, BC, AC Step 2. Write the angles opposite those sides. C, A, B

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. Ex. 2 Write the measurements of the sides in order from least to greatest. Step 1. List the angles in order from least to greatest. X, Z, Y Step 2. Write the sides opposite those angles. Y YZ, XY, XZ 128º X 22º 30º Z

Right Triangles hypotenuse leg leg hypotenuse In a right triangle, the ___________ is the side with the greatest measure.