Unique Triangles--Two Sides and a Non-Included Angle

Students understand that two sides of a triangle and an acute angle not included between the two sides may not determine a unique triangle. Students understand that two sides of a triangle and a 90° angle (or obtuse angle) not included between the two sides determine a unique triangle. A triangle drawn under the condition of two sides and a non-included angle is often thought of as a condition that does not determine a unique triangle. Students see that the sub-condition, two sides and a non-included angle, provided the non-included angle is an acute angle, is the only sub-condition that does not determine a unique triangle.