# Triangle Theorems Triangle Inequalities, Hinge Theorem, Exterior Angle Theorem

In this lesson, I will talk about triangle inequalities, exterior angle, and hinge theorem. These theorems can help us arrange the sides and angles of a triangle from smallest to largest.

##### What is the triangle inequality theorem?

This states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

##### What is the Exterior Angle Theorem?

The measure of an exterior angle is equal to the sum of two remote interior angle.

##### What is the Hinge Theorem

If two triangles have two sets of congruent sides, the larger included angle will have the longer third side.

###### Useful Resources

Practice what you’ve learned in these problems.

Exercises 1

Exercises 2

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