Unit
Triangles
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
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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.