Theorems and Postulates
Brice Chen
Triangle Sum theorem
The sum of all of a triangles angles is 180 degrees, in euclidean geometry.
I chose this theorem because it is needed for almost all problems asking you to solve for x in angles.
Sas congruence theorem
If two sides and the included angle of another triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent.
I chose this theorem since it is one of the most common ones used in most occasions.
Asa Congruence Theorem
If two angles and the included side of one triangle are congruent to two
angles and the included side of another triangle, then the triangles are congruent.
angles and the included side of another triangle, then the triangles are congruent.
This one was chosen because it is commonly confused with the next one about to be shown.
AaS Congruence Theorem
If two angles and a nonincluded side of one triangle are congruent to
the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.
the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.
This congruence is different, instead of the congruent sides being in between the angles, it only touches one angle. You can find out which one it is by following the edge of the triangle around starting from one angle and tracing along one side to the other angle. If you go over the congruent line mark, then it is ASA, if not, then AAS.