s proving triangles congruent ss. s as a sa a as this one is a theorem!!

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SS

Proving Triangles CongruentProving Triangles Congruent

SSSS

SS

Proving Triangles CongruentProving Triangles Congruent

AASS

AA

Proving Triangles CongruentProving Triangles Congruent

SSAA

AA

Proving Triangles CongruentProving Triangles Congruent

AASS This one is a THEOREM!!

Proving Triangles CongruentProving Triangles Congruent

HHLL This one is a THEOREM!!

CAUTION!!CAUTION!!

BE CAREFUL!!!NOT ALL combinations S & A will give congruent triangles.

AAAAAA•AAA is NOT a method to

prove two triangles congruent. It will show two triangles that have the same SHAPE, but NOT necessarily the same SIZE!!

SSA (OR ASS)SSA (OR ASS)• This is humorously

referred to as the Donkey Theorem. It is NOT a valid way to show two triangles are congruent!!

1

LKN LMN by SAS Postulate

2

Not Congruent

3

FGH JKL by SAS Postulate

4

LKN LMN by SAS Postulate

5

Not Congruent

6

XYZ TUV by SSS Postulate

7T

E G

I

R

ERT IRG by ASA Postulate

Vertical Angles Theorem

Alternate Interior Angles Theorem

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