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)
