Conditions for a Unique Triangle―Two Angles and a Given Side

Students understand that two triangles are identical if two pairs of corresponding angles and one pair of corresponding sides are equal under some correspondence; two angle measurements and a given side length of a triangle determine a unique triangle. Students understand that the two angles and any side condition can be separated into two conditions: (1) the two angles and included side condition and (2) the two angles and the side opposite a given angle condition. In Lesson 9, students learned two conditions that determine unique triangles: the three sides condition and the two sides and included angle condition. Drawing several examples of triangles under these conditions demonstrated that there was only one possible configuration of a triangle to be drawn.