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5.6 Triangle Inequality Worksheet
Name: ________________________
Things to remember: For any triangle, the sum of the lengths of any two sides is greater than the
length of the third side. | AND | for any triangle, if two sides are not congruent, then the larger
angle is opposite the longer side
1. Can a triangle have side lengths 22, 33, and 25? Why or why not? Show your work.
2. Can a triangle have side lengths 3, 7, and 11? Why or why not? Show your work.
3. Two sides of a triangle are 15 ft and 12 ft. What could be the length of the third side?
4. Order the angles of the triangle from SMALLEST to LARGEST. (Hint: start by ordering the
sides smallest to largest)
5. Order the sides of the triangles from LONGEST to SHORTEST.
6. Determine the Longest side of ∆MNO, where mM = 56, mN = 108, and mO = 16.
7. List the sides in order from shortest to longest in ∆XYZ:
with mX = 50, mY = 5x + 10, and mZ = 5x.
8. Mr. Cuddy draws a triangle with a perimeter 36 cm. Principal Aranda says that the longest side
measures 18 cm. How do you know that the Principal Aranda is incorrect? Explain.