ASA and AAS - Problem 4


When you are looking at two triangles that share a common side, the easiest way to determine if they are congruent is to redraw one of the triangles. So that's what I’m going to do here because I can’t tell just by looking at this if we have enough information.

So I’m going to redraw this triangle, DAC, down below and I’m going to make it look just like our lower triangle ABC. So which angle corresponds to A? Well angle C here has our 90 degree angle. Angle B corresponds to angle D because there are no markings on that angle, which means our last angle over here is angle A. So I’m going to write that with two markings.

So now the question is do we have enough information? I know that these two corresponding angles are congruent, I know that threes two angles are corresponding and congruent, but that’s not enough information. As I said in the beginning we have a shared side, AC must be congruent to itself; that’s called the reflexive property. So notice that we have angle, an included side and an angle that’s enough information to say that these two triangles must be congruent. So I’m going to write by angle-side-angle, which is our congruent short-cut.

The second step is to say well what corresponds to angle A? Angle A, because I’ve redrawn it it’s pretty easy to see that C corresponds to angle A. Angle B which comes second corresponds to angle D, and last angle C corresponds to angle A.

So the trick to this problem is to redraw this top triangle below so that you can compare the triangles pretty easily.

triangle congruence angle side angle angle angle side