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Triangle Inequality Theorem Worksheet

A Grade 12 math worksheet focusing on the Triangle Inequality Theorem, including identifying valid triangles, determining possible side lengths, and working with algebraic expressions.

Grade 12 Math GeometryTriangle Inequality Theorem
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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10

Topics

mathgeometrytriangleinequalitygrade 12
7 sections · Free to use · Printable
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Triangle Inequality Theorem

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Read each question carefully and apply the Triangle Inequality Theorem to determine the correct answers. Remember that 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 CANNOT form a triangle?

a

3, 4, 5

b

6, 8, 10

c

2, 3, 6

d

7, 7, 7

2. If two sides of a triangle are 12 cm and 17 cm, which of the following could be the length of the third side?

a

4 cm

b

5 cm

c

29 cm

d

30 cm

3. For a triangle with side lengths a, b, and c, the Triangle Inequality Theorem states that a + b > c, b + c > a, and a + c >  .

4. If the lengths of two sides of a triangle are 9 units and 15 units, the length of the third side must be greater than   units and less than   units.

5. A triangle has side lengths of (x + 2), (2x - 1), and (x + 5). Determine the possible range of values for x.

6. Can a triangle have side lengths of 4.5 inches, 6.2 inches, and 10.8 inches? Justify your answer using the Triangle Inequality Theorem.

7. A triangle with side lengths 1, 1, and 1 can be formed.

T

True

F

False

8. If the sum of two side lengths of a triangle is equal to the third side length, then a triangle can still be formed.

T

True

F

False

9. Consider a triangle with two sides measuring 8 units and 13 units. Let the third side be 's'. Write an inequality that represents the possible range of values for 's'.

10. Two sides of a triangle are 10 cm and 24 cm. If the third side is an integer, how many possible integer lengths are there for the third side?