Geometry Help on Congruent Triangles!!!!!?

Question

I know that I use SSS, SAS, ASA, HL, and AAS to see if two triangles are
congruent. I also know that SSA is not supposed to be used. The basic way
to use it is using HL, with a right triange. I also was told there was
another example of two congruent traingles with SSA that are not right
triangles.

Answer 1

SSA holds when the first "S," the side opposite the angle, is at least the size of the second side. (It does not hold otherwise.)

This holds true for the special case (HL). The hypotenuse is always longer than the leg.

Answer 2

The SSA (Side-Side-Angle) condition does not guarantee congruence, because it is possible to have two incongruent triangles that satisfy the SSA conditions (two congruent corresponding sides and a congruent non-included angle). This is known as the ambiguous case. Specifically, SSA is not valid if the angle is acute and the first side (the side opposite to the angle) is at the same time shorter than the second side and longer than the second side times the sine of the angle. In all other cases the criteria SSA is valid.

Thus, the SSA condition does prove congruence when the angle is a right angle. This is known as the HL (Hypotenuse-Leg) condition, or the RHS (Right Angle-Hypotenuse-Side) condition. This is true because the hypotenuse of a right triangle is always longer than either leg.

The SSA condition is also valid if the angle is obtuse; or if the first side equals the second side times the sine of the angle (in which case it is a right triangle). (For comparison notice that the first side cannot be smaller than the second side times the sine of the angle as the triangle will not "close".)