SOLUTION: what are all of the types of triangle congruencies

Question 687607: what are all of the types of triangle congruencies
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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) (Show Source): You can put this solution on YOUR website!

Congruence between two triangles means , all and all , are .

-all types of triangle congruencies represented by the triangle congruence are:
, , (which is the same as and is usually referred to as ), and

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

If in two triangles the are pairwise , then the triangles are congruent.
2.
is more formally known as the Triangle Congruence Theorem:
If in triangles sides and the included angle are pairwise , then the are .
3.
is more formally known as the Triangle Congruence Theorem:
If in triangles angles and a side are pairwise , then the triangles are .
4.
is more formally known as the Triangle Congruence Theorem:
If in triangles angles and included sides are pairwise , then the triangles are .

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