5.5 Inequalities in One Triangle

To apply inequalities in one triangle

This can help someone to find a reasonable range of values for unknown distances.

Directions: With your partner, make a conjecture about the following situation.

1) Given: ST = 7, TV = 12, and SV = 15

Order the angles from smallest to largest.

2) Given: mS =40°, mT = 85°, mV = 55°

Order the sides from smallest to largest.

3) Summarize your findings from 1 and 2.

Example 1: Write the angles in order from Example 2: Write the sides in order from

smallest to largest. smallest to largest.

Example 3: Write the angles in order from Example 4: Write the sides in order from

smallest to largest. smallest to largest.

A triangle is formed by three segments, but not every set of three segments can form a triangle…

Theorem Hypothesis Conclusion

Triangle Inequality Theorem

The sum of any two ___________

lengths of a triangle is ____________

than the ___________side length.

Directions: Tell whether a triangle can have sides with the given lengths. Explain why or why not.

Example 5: 3, 5, 8 Example 6: 11, 15, 22

Example 7: 7, 10, 19 Example 8: n + 6, n2 – 1, 3n when n = 4

TIP: Given the lengths of _____ sides of a triangle, the length of the ______ side must be less than their sum

but greater than their positive difference. This is especially helpful if you are given two sides of a triangle and

want to know what the possibilities are for the length of the third side.

Example 9: Consider a triangle with sides a, b, and c. Example 10: The figure below shows the

approximate distances

If a = 10 and b = 3, what are the possible between cities is California.

lengths for side c? What is the range of distances

from Oakland to San Francisco?