Applied Geometry Lesson 7 4 Triangle Inequality Theorem

Applied Geometry Lesson: 7 – 4 Triangle Inequality Theorem Objective: Learn to identify and use the Triangle Inequality Theorem.

Using a ruler draw a triangle with the following measurements (cm). 5, 7, 4 1, 1. 5, 3 11, 3, 7 16, 10, 5 3, 4, 5 7, 10, 12

Triangle Inequality Theorem The sum of the measures of any two sides of a triangle is greater than the measure of the third side.

Determine if the three numbers can be measures of the sides of a triangle. 5, 7, 4 5+7>4 7+4>5 5+4>7 Yes, it is a triangle. 11, 3, 7 11 + 3 > 7 3 + 7 > 11 No, it is not a triangle. 16, 10, 5 16 + 10 > 5 10 + 5 > 16 No, it is not a triangle.

What are the greatest and least possible whole number measures for the 3 rd side? x Write the 3 inequalities. 10 + 7 > x 10 + x > 7 17 > x x > -3 7 + x > 10 x>3 Can’t have a negative side. x has to be less than 17, but greater than 3. So the greatest and least WHOLE NUMBER measures are 16 cm & 4 cm.

What are the greatest and least possible whole-number measures for the third side of a triangle if the other two sides measure 8 inches and 3 inches? 8+3>x 11> x 3+x>8 x>5 10 inches & 6 inches.

4+4>x 8>x 4+x>4 x>0 The measure of the third side is bigger than 0, but less than 8 0<x<8

If the measures of two sides of a triangle are 9 and 13, find the range of possible measures of the third side. 9 + 13 > x 22 > x 9 + x > 13 x>4 4 < x < 22

Homework Pg. 298 1 – 8 all, 10 – 30 E