Which triangles are possible

Decide whether given side and angle conditions determine a unique triangle, more than one triangle, or no triangle, and explain why, predicting with a freehand sketch and testing by construction (ruler and protractor, compasses, or dynamic geometry software): three sides give exactly one triangle when each pair of sides adds to more than the third, and none otherwise — if the two shorter sides add to less than the longest, the construction arcs do not meet, and if they add to exactly the longest (e.g. 3, 4 and 7), the arcs touch only on the base line, so the sides lie flat in a straight line rather than forming a triangle; three angles must add to 180° and then fix only the shape, not the size, so many triangles fit (none if the sum is not 180°); two sides with the included angle, or two angles with the included side, give exactly one triangle; and two sides with an angle that is not between them can give two, one or no triangles