Question

Which statement explains why ABC is congruent to A A'B'C' ?

Answer 1

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

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.