Triangle Inequality Theorem Worksheet

Explore the Triangle Inequality Theorem with this Grade 7 worksheet, featuring questions on identifying valid triangles and determining possible side lengths.

Grade 7 Math GeometryTriangle Inequality Theorem

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Includes

Multiple ChoiceFill in the BlanksTrue / FalseShort Answer

Standards

CCSS.MATH.CONTENT.7.G.A.2

Topics

mathgeometrytrianglesinequalitygrade 7

6 sections · Free to use · Printable

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Triangle Inequality Theorem

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Read each question carefully and answer to the best of your ability. Remember the 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.

1. Which set of side lengths CAN form a triangle?

2 cm, 3 cm, 6 cm

4 cm, 5 cm, 9 cm

5 cm, 7 cm, 10 cm

1 cm, 2 cm, 3 cm

2. If two sides of a triangle are 8 inches and 12 inches, which of the following could be the length of the third side?

3 inches

4 inches

20 inches

15 inches

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

4. If a triangle has sides of length 7 units and 10 units, the third side 'x' must satisfy the inequality: < x < .

5. A triangle can have side lengths of 5 cm, 5 cm, and 10 cm.

True

False

6. If the sides of a triangle are a, b, and c, then a + b > c, a + c > b, and b + c > a must all be true.

True

False

7. A triangle has two sides with lengths 6 inches and 10 inches. Write an inequality that represents the possible lengths for the third side, x.

8. Can a triangle have side lengths of 15 ft, 8 ft, and 7 ft? Explain your reasoning using the Triangle Inequality Theorem.