Lesson: 7 – 4 Triangle Inequality Theorem

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Presentation transcript:

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 11, 3, 7 3, 4, 5 1, 1.5, 3 16, 10, 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.

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

So the greatest and least WHOLE NUMBER measures What are the greatest and least possible whole number measures for the 3rd side? x Write the 3 inequalities. 10 + 7 > x 10 + x > 7 7 + x > 10 x > 3 17 > x 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.

10 inches & 6 inches. 8 + 3 > x 3 + x > 8 x > 5 11> x 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 3 + x > 8 x > 5 11> x 10 inches & 6 inches.

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

9 + 13 > x 9 + x > 13 22 > x x > 4 4 < x < 22 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 9 + x > 13 22 > x x > 4 4 < x < 22

Homework Pg. 298 1 – 8 all, 10 – 30 E