# Triangle Inequality Theorem - Inequalities in Triangles

Worksheet (Geometry)

## Triangle Inequality Theorem - Inequalities in Triangles Worksheet

This free geometry worksheet contains problems on the properties of inequalities in triangles - including the Triangle Inequality Theorem (the sum of the lengths of any two sides of a triangle is greater than the length of the third side). Students must apply these properties and relate them to the sides and angles of triangles.

## Lesson:

5. To use the triangle inequality theorem

15

4

Yes

## Samples:

Inequalities in Triangles

Complete each Inequality Theorem.

1) If one side of a triangle is longer than a second side, then the larger angle lies opposite the _____________ side.

2) If one angle of a triangle is larger than second angle, then the longer side lies opposite the _____________ angle.

3) The sum of the lengths of any two sides of a triangle is _____________ than the length of the third side.

4-5) Name the largest angle and the smallest angle of each triangle.

6-7) Name the largest angle and the smallest angle of each triangle. Is it possible for a triangle to have the sides with the lengths indicated? Explain.

8) 3, 7, 8

9) 1, 1, 4

10) 9, 6, 2

11) 3, 4, 5

12) 2.4, 2.9, 5

13) 3, 6, 10

14) Two sides of a triangle have lengths of 10 and 13. The length of the third side can be any number between _____ and ______.

15) Two sides of a triangle have lengths of 5x and 11x. The length of the third side can be any number between _____ and ______.

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