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# ASA and AAS - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

If two triangles are congruent, all three corresponding sides are congruent and all three corresponding angles are congruent. If two pairs of corresponding angles and the side between them are known to be congruent, the triangles are congruent. This shortcut is known as angle-side-angle (ASA). Another shortcut is angle-angle-side (AAS), where two pairs of angles and the non-included side are known to be congruent. **ASA and AAS** are important when solving proofs.

Congruence shortcuts. What are they? Basically when you have two different triangles and you're trying to determine are the 3 angles of these two triangles congruent? And are the 3 sides congruent? We don't need to know all 6 items.

One shortcut is angle side angle, so what does that mean angle side angle? Well what it means is if you have one triangle and I tell you that these two corresponding angles are congruent, and if an included side is congruent, well what do I mean by included? Well I mean that this other angle here that is adjacent to that side that these two angles must be congruent so I know an angle I have the side and an angle so that is called the angle side angle shortcut. All you need to know are these 3 items and you can say yes these two triangles must be congruent.

But there's one other one that we're going to talk about and that is angle angle side so I'm going to erase these markings just so we can draw our comparison, so angle angle side says that if you know about these two triangles are two angles and a non included side so what's difference about this is I could say that these two angles are congruent but the side that I know is not in between the two angles. The side that I know has to be non included so could be over there or it could also be on the other side. These are both angle angle side, angle angle side. That's all you need to know and you can say that these two triangles must be congruent.

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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

so my teacher can't explain this in 5 weeks but I learn this in less than 3 minutes”

its hard to focus when the teacher is really really really goodlooking”

i like how it took you 3 minutes and 8 seconds to accomplish what my teacher couldn't in 3 days”

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## Comments (3)

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## jannah · 1 month ago

Nice explanation Brian McCall

## Richard · 5 months ago

I did share my thoughts, and I did do so rather nicely. Relevant facts specific to the discipline are always nice. Questioning is an important component of learning.

## Richard · 5 months ago

AAS and ASA ... Each case is inherently redundant with respect to the other. AAS? ... if we know two pair of corresponding angles are congruent, the triangle sum theorem guarantees that the remaining third corresponding pair of angles must be congruent as well. Thus, the known pair of corresponding sides of the scenario can then be seen as "included" sides, and the scenario becomes a clear case of ASA. ASA? ... ASA can be shown in similar fashion to reduce to a clear case of AAS. Why are two cases necessary where one will do? Convention for its own sake is not meaningful. Understanding trumps rote application.