GH­­Lesson 5­5_notes.notebook November 03, 2015

5­5 The Triangle Inequality

Students will be able to use the Triangle Inequality Theorem to identify possible triangles.

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

A

BC a

b c

a + b > c

b + c > a

a + c > b

GH­­Lesson 5­5_notes.notebook November 03, 2015

Triangle Inequality Theorem is used to . . .

(a) determine if three lengths can form a triangle

­­Verify all three inequalities are true

(b) find a range of values for a third side, given the two other sides of the triangle.

­­Write the three inequalities and solve. Eliminate any inequality that would result in negative segment lengths.

Write the answer as a compound inequality.

minimum value < variable < maximum value

GH­­Lesson 5­5_notes.notebook November 03, 2015

determine if three lengths can form a triangle

­­Verify all three inequalities are true

GH­­Lesson 5­5_notes.notebook November 03, 2015

find a range of values for a third side, given the two other sides of the triangle.

­­Write the three inequalities and solve. Eliminate any inequality that would result in negative segment lengths.

Write the answer as a compound inequality!

GH­­Lesson 5­5_notes.notebook November 03, 2015

Additional Examples

Determine the range of possible values for x.

(b) What is the range of possible perimeters of ΔABC?

(a)