Using the triangles shown, explain how the SAS congruence criteria follows from the definition of congruence in terms of rigid motions.
simple answer
The SAS (Side-Angle-Side) congruence criteria states that if two triangles have two sides and the included angle between them equal, then the two triangles are congruent. This can be easily explained using the definition of congruence in terms of rigid motions.
Two triangles are said to be congruent if one can be transformed into the other by a combination of translation, rotation, and reflection. This means that the two triangles have the same shape and size.
Now, if two triangles have two sides and the included angle between them equal, then we can rotate and translate one triangle to place it on top of the other. The two triangles will then have the same shape and size, satisfying the definition of congruence.
Therefore, the SAS congruence criteria follows from the definition of congruence in terms of rigid motions.