### Midsegment Theorem

A midsegment of a triangle is parallel to the third side and is half as ling as the third side

### Third Angle-Side Relationships Theorem

The longest side of a triangle is opposite the largest angle and the shortest side of a triangle is opposite the shortest angle

### Exterior Angle Inequality Theorem

The measure of an exterior angle of a triangle if greater than the measure of either of the two nonadjacent sides

### Triangle Inequality Theorem

The sum of the length of any tow sides of a triangle if greater than the length of the third side

### The Hinge Theorem

If 2 sides of a triangle are congruent to 2 sides of another triangle but the angles between the sides have different measures, then the third sides of each triangle compare the same as the angles

### The Hinge Theorem Converse

If two sides of one triangle are congruent to two sides of another triangle, but the third sides have different measures, then the angle between the first two sides compare the same as the third sides

### Triangle Centroid Theorem

The centroid cuts each medians length so that the segment from the vertex is 2/3rds of the medians length and the segment to the side if 1/3rd of the medians length