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Six facts that are true about two congruent triangles.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
Congruent triangles have:
- three congruent (equal ) sides
- three congruent (equal) angles
4
4
4
4
4
4
Congruent
Equal sides and angles
Not Congruent
Equal angles but not equal sides
In order to take the guess work out of proving if triangles are congruent there are five methods used to prove if the triangles are congruent
Proving Triangles Congruent/ Side Side Side
HL
Angle Side Angle
Hypotenuse Leg
Angle Angle Side
AAS
ASA
SSS
SAS
SSS The three sides of one triangle are congruent to the three sides of another triangle
Side Angle Side
SAS Side Angle Side The two sides plus the included angle of one triangle are congruent to the two sides plus the included angle of another triangle
ASA Two angles and the included side of one triangle is congruent to two angles and the included side of another triangle. The side between the two angles being used is the included side.
AAS Two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle. Either side that is not between the two angles being used is can be a non-included side
HL Hypotenuse leg The hypotenuse and leg of one right triangle is congruent to the hypotenuse and leg of another triangle
Proving Triangles Congruent
Click on the picture for the full size "Proving Triangles Congruent" Infographic
Proving Triangles Congruent
Proving Triangles Congruent/Infographic
CPCTC is an acronym for corresponding parts of congruent triangles are congruent. This theorem states that once two triangles are proven to be congruent, then the three pairs of sides and angles that correspond must be congruent. The following video shows how to use CPCTC