In this activity we examine the AA and AAA triangle conditions in Euclidean Geometry. [br][br]Manipulate the sliders and/or input boxes to select the measures of two of the interior angles of the triangle. Note that the text boxes take the angles in radians, but the angles are also displayed in degrees.[br][br]What conditions on these two angles will prevent a triangle from being constructed?[br]What conditions on the two angles guarantee that at least one triangle can be constructed? [br]If a triangle is possible, then what can we say about the third angle?[br][br]Slowly slide the step slider until we get to step 6. Manipulate the orange points. How many shapes and sizes (congruence classes) for these triangles are possible with these 2 given angle measures?[br][br]If we have two triangles with 3 corresponding pairs of congruent angles, is that enough to conclude that the triangles are congruent?[br][br]Manipulate the controls above to discover something we can say about the side lengths.[br]