AAS: If Two angles and a side opposite to one of these sides is congruent to the
corresponding angles and corresponding side, then the triangles are congruent.
How Do I know? Taking Geometry right now. :)
The answer will depend on the two triangles in question. Since that information is not provided it is not possible to give a sensible answer.
The answer depends on what you mean by equal. Equal in area? Congruent?
SAS
Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
SAS
We definitely need to see the drawing that goes along with that question before we can even begin to try and answer it.
HL congruence theorem
It is a theorem, not a postulate, since it is possible to prove it. If two angles and a side of one triangle are congruent to the corresponding angles and side of another triangle then the two triangles are congruent.
SAS
ASA
Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
The first thing you prove about congruent triangles are triangles that have same side lines (SSS) is congruent. (some people DEFINE congruent that way). You just need to show AAS is equivalent or implies SSS and you are done. That's the first theorem I thought of, don't know if it works though, not a geometry major.
It does not necessarily prove congruence but it does prove similarity. You can have a smaller or bigger triangle that has the same interior angles.
Excuse me, but two triangles that have A-A-S of one equal respectively to A-A-S of the other are not necessarily congruent. I would love to see that proof!
BAD = BCD is the answer i just did it
ASA
SAS
Blah blah blah