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
By ASA, if two angles and the side between them are congruent two corresponding angles the side between them, then the two triangles are congruent. By AAS, if two angles and a side of a triangle are congruent to two angles and a side of another triangle, the two triangles are congruent. The position of the angles and side is important--the side must either be between the two angles in both triangles, or beside one of the angles in both triangles (you cannot use both ASA and AAS at the same time to say that two triangles are congruent). It is important to check if the angles and sides in question are correspondent in order to show congruence.
If there is not enough information, such as the congruence of certain angles or sides, the congruence of the triangles cannot be determined.
Something I always tell my geometry students is you can’t assume anything just by looking at a picture. So it looks like we have a parallelogram here, but it’s not marked that these two sides are parallel, nor are the other two sides. So we can’t assume that there is anything parallel in this problem. And it's asking triangle ABD is congruent to this other triangle, but how?
Well to start off I’m going to redraw this triangle down below just so they correspond. It makes it a little but easier for us to determine if we have enough information. So I see angle A has three markings. So I’m going to write angle D, so they correspond, because angle D has three congruence markings. If I look at angle B, angle B has two congruence markings and that corresponds to C, so I’m going to write C as my top vertex, which leaves our bottom as B.
So all we know right now is that these two angles are corresponding and congruent,but notice that they share this side BD, so I’m going to say that BD is congruent to BD. A little red flag should go off in your mind right now.
Mr. McCall we’ve got angle-angle-side in that triangle we’ve got angle-angle-side in this triangle, but notice that these two sides are not correspondent. If you look, if CB was congruent to BD, then yes we would have enough information. As such because DB does not correspond in these two triangles I’m going to write this cannot be determined, which means we do not have enough information to say that these two triangles must be congruent.