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
Well, this will depend on the length of the sides of the triangle for what postulate or theorem you will be using.
AAS: If Two angles and a side opposite to one of these sides is congruent to thecorresponding angles and corresponding side, then the triangles are congruent.How Do I know? Taking Geometry right now. :)
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.
To prove that triangle SEA is congruent to another triangle, you can use the Side-Angle-Side (SAS) Postulate. This postulate states that if two sides of one triangle are equal to two sides of another triangle, and the angle included between those sides is also equal, then the triangles are congruent. Additionally, if you have information about the angles and sides that meet the criteria of the Angle-Side-Angle (ASA) or Side-Side-Side (SSS) congruence theorems, those could also be applicable.
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!
AAS: If Two angles and a side opposite to one of these sides is congruent to thecorresponding angles and corresponding side, then the triangles are congruent.How Do I know? Taking Geometry right now. :)
To prove the Isosceles Triangle Theorem using a figure, the best strategy is to focus on the properties of the triangle's angles and sides. Start by labeling the two equal sides and their opposite angles. Then, use triangle congruence criteria, such as the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA), to establish that the two triangles formed by drawing a line from the vertex to the base are congruent. This congruence will demonstrate that the base angles are equal, thereby proving the theorem.
BAD = BCD is the answer i just did it
ASA