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In order to prove that the triangles are congruent by SAS, we need two congruent pairs of sides and the angles between these sides also congruent.
Let's analyze each sentence:
A.
We need one pair of congruent angles, with this proff we would have the angle needed, but the question didn't say the triangle is isosceles. This theorem states that the opposite angles to the congruent sides in a isosceles triangle are congruent.
B.
We still don't know that the triangles are congruent, so we can't use the reason CPCTC.
C.
These angles are not vertical angles.
D.
With this statement we have one of the required pair of congruent sides to prove the triangles congruent.
Therefore the correct option is D.
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