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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?