# What is the Hinge Theorem?

#### Understand the Problem

The question is asking for an explanation of the Hinge Theorem, which is a concept in geometry that relates to the comparison of the lengths of sides of triangles when the angles are known. The Hinge Theorem states that if two triangles have two sides of equal length and the included angle of one triangle is larger than that of the other triangle, then the side opposite the larger angle in the first triangle will be longer than the side opposite the smaller angle in the second triangle.

#### Answer

In two triangles, the triangle with the larger included angle between two congruent sides has a longer third side.

The Hinge Theorem states that in two triangles, if two sides of one triangle are congruent to two sides of another triangle, but the included angles are different, then the triangle with the larger included angle will have a longer third side compared to the third side of the triangle with the smaller included angle.

##### Answer for screen readers

The Hinge Theorem states that in two triangles, if two sides of one triangle are congruent to two sides of another triangle, but the included angles are different, then the triangle with the larger included angle will have a longer third side compared to the third side of the triangle with the smaller included angle.

#### More Information

The Hinge Theorem is also known as the SAS (Side-Angle-Side) Inequality Theorem and is useful in comparing side lengths in triangles.

#### Tips

A common mistake is to confuse which side is opposite which angle. Ensure you are correctly identifying the sides and angles.

#### Sources

- Hinge theorem - Yup Math - yup.com
- Hinge Theorem - MathBitsNotebook (Geo) - mathbitsnotebook.com
- Hinge Theorem - Wikipedia - en.wikipedia.org