1. 5-3 Inequalities and Triangles The student will be able to: 1. Recognize and apply properties of inequalities to the measures of the angles of a triangle. 2. Recognize and apply properties of inequalities to the relationships between the angles and the sides of a triangle.

2. Remember the Exterior Angle Theorem? Now, we have the Exterior Angle Inequality Theorem. If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its remote interior angles. So, and Hint: Look for the exterior angle and identify its remote interior angles. Exterior angle = the sum of the two remote interior angles. Exterior angle Remote Interior angles

3. Name all angles that satisfy the conditions. What triangle(s) is  1 an exterior angle for? The remote interior angles are <  1. What triangle is  1 inside of? The exterior angle(s) of that triangle is/are >  1.  UWT. What triangle(s) is  7 an exterior angle for?  UWV.  UWT &  UVT. The remote interior angles are <  7. Hint: Separate the triangles so it will be easier to identify the exterior/remote interior angles.

4. If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. If one angle of a triangle has a greater measure than another angle, then the side opposite the greater measure is longer than the angle opposite the shorter side. If, then.

5. List the sides or angles in order from least to greatest. If we know the measure of the ANGLES then we can tell which SIDES are greater than or less than others. If we know the measure of the SIDES then we can tell which ANGLES are greater than or less than others.

6. Determine the relationship between the angles: < 35 13 + 25 22 35 < 21.6 > How long is the side opposite  R? How long is the side opposite  RUS? How long is the side opposite  UST? How long is the side opposite  T? How long is the side opposite  UVS? How long is the side opposite  USV?

7. Determine the relationship between the lengths of the given sides: 90° 30° > 60° 30° > 60° 90° < How long is the angle opposite ?