SOLUTION: what are all of the types of triangle congruencies

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Question 687607: what are all of the types of triangle congruencies
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
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AAS: Angle Angle Side
ASA: Angle Side Angle
SAS: Side Angle Side
SSS: Side Side Side
HL: Hypotenuse Length

Note: SSA is NOT a valid congruence property. Also, you need at least one side. So you cannot use angles only.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Congruence between two triangles means six+items, all three sides and all three+angles, are congruent.

-all types of triangle congruencies represented by the four triangle congruence theorems are:
+SSS, SAS, SAA (which is the same as and is usually referred to as AAS), and ASA

1.
SSS is more formally known as the Side-Side-Side Triangle Congruence Theorem:

If in two triangles the three+sides are pairwise congruent, then the triangles are congruent.
2.
SAS is more formally known as the Side-Angle-Side Triangle Congruence Theorem:
If in 2 triangles 2 sides and the included angle are pairwise congruent, then the triangles are congruent.
3.
AAS is more formally known as the Angle-Angle-Side Triangle Congruence Theorem:
If in 2 triangles 2 angles and a non-included side are pairwise congruent, then the triangles are congruent.
4.
ASA is more formally known as the Angle-Side-Angle Triangle Congruence Theorem:
If in 2 triangles 2 angles and included sides are pairwise congruent, then the triangles are congruent.