Which statement explains why abc is congruent to a a'b'c' ?

The two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.

Step-by-step explanation:

Rigid Transformation is a transformation which PRESERVES (keeps it SAME) the LENGTH and the ANGLES in an image and pre- image.

Here, as we can ΔABC goes under Rigid Transformation in to the ΔA'B'C'

⇒Sides AB, BC and AC correspond to the sides A'B',B'C' and A'C' respectively.

Also the ∠A, ∠B and∠C correspond to  ∠A', ∠B' and∠C' respectively.

Now, in  ΔABC and ΔA'B'C

AB  = A'B'

BC  =   B' C'

AC  = A'C'

⇒The two given triangles are congruent by SIDE SIDE SIDE property.

Also, ∠A  = ∠A'

∠B  =   ∠B'

⇒The two given triangles are congruent by ANGLE ANGLE property.

Hence the two given triangles ABC and A'B'C' are congruent by SSS or AA axiom of congruence.