Congruent triangles criteria
Investigate the different triangles generated by fixing various measurements (eg two sides and the angle in between). Change the values with the sliders to see how the triangles change. Notice that it is sometimes possible to generate two different triangles with two sides and an angle when that angle is not in between the two sides.
Congruent triangles are the same shape and the same size (although they may be reflections or rotations of one another). The SSS criteria means that two triangles are congruent if all corresponding sides are equal. The SAS criteria means that two triangles are congruent if two corresponding sides and the angle in between are equal. The ASA criteria means that two triangles are congruent if two corresponding angles and the side in between are equal. The RHS criteria means that two triangles are congruent if they are both right-angled triangles, their hypotenuses are equal, and one other side is equal. Note: This is a special case of the ASS criteria below, which does not give congruent triangles in general) The last one, the ASS criteria - two corresponding sides and a corresponding angle are equal - does not prove congruence. As demonstrated, there are often two possible triangles that can be created while still fulfilling the criteria.