![]() Same thing goes with the angle angle side shortcut. ![]() The reason being is that if you know that these two angles are congruent, then that is just using the angle angle shortcut. Now if I were to compare these two lists, you're going to notice that I omitted angle side angle. So we're going to say that side side side is also a shortcut. These 2 triangles would also have to be congruent. So we could write out this proportion that that is constant between corresponding sides. And last let's say, if all we knew were that 3 sides of 2 different triangles, that correspond, are proportional. So we're going to include side angle side into our list of similarity shortcuts. Well this would be enough information to say that these two triangles are similar. And you also knew that the corresponding sides are proportional. Let's say that all you knew were a side an included angle and another side. The reason being is if all you know are 2 angles, that's enough information because that third angle which I guess I could write in has to be congruent as well. Now notice that I did not write angle angle angle. We're going to say that angle angle is a shortcut. So under our similarity shortcuts, I'm going to use a different marker here. Which means that corresponding angles are congruent and corresponding sides are proportional. And yes this would be a shortcut for saying that these 2 triangles must be similar. But the triangle angle sum, if these two angles are congruent, then the third angle in each of these triangles must be congruent. Let's start off by looking at a case where all we know about two triangles is that 2 angles are congruent. We're going to draw a comparison with similarity. So these these two shortcuts did not give you enough information to say that these two triangles must be congruent because using only three angles you could construct two triangles that are not the same size. And those were angle angle angle and side side angle. ![]() So if you knew just three things about those two triangles, if it's one of these shortcuts, then yes you could say these triangles must be congruent. ![]() And those 4 shortcuts were angle side angle, side angle side, side side side and angle angle side. We said that there were 4 shortcuts for proving two triangles congruent. If you were to prove that two triangles are similar, we're going to draw a comparison with congruence, something that we talked about previously. ![]()
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