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
In order to determine how two triangles are congruent, one must first determine if there is enough information to say whether or not they are. To see if there are congruent angles, use other concepts from geometry. Recall that vertical angles, alternate interior angles, alternate interior angles, and alternate exterior angles are congruent.
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).
When you see a problem like this where you have two different triangles and they give you one triangle to have little Mr.Squiggles here which means congruence. What you’re trying to assess is, are there enough information between these two triangles to say that they are congruent?
Well if I look at this I have two corresponding angles that are congruent and I have two corresponding sides that are congruent. Unfortunately none of our congruent short-cuts work for just an angle and a side. So there has to be one other piece of information.
Well I see that right here we have vertical angles. We know vertical angles must be congruent. So what I’m going to do is I’m going to write in that these two angles must be congruent. So now we have enough information to say definitively that these two triangles must be congruent.
And what’s going to be our short-cut? Well we have an angle in included side with another angle. So right down here I’m going to say by angle-side-angle, always say what’s your congruent short-cut. Now let’s say well what corresponds with A?
Well A has this one mark of congruence; E has one mark of congruence so vertex A corresponds to vertex E. Vertex is this vertex that doesn’t have any marking. Well on this triangle that’s vertex D. So D is going to come next. And last C corresponds with two congruence markings and C corresponds with two congruence markings.
So triangle ABC congruent to triangle EDC, all you have to do is see do you have enough information to use to use a short-cut? If so then yes these two triangles must be congruent.
