Which statement is true about the two triangles in the diagram?
a) the triangles are congruent, proven by asa.
b) the triangles are congruent, proven by aaa.
c) the triangles are congruent, proven by hl.
d) the triangles are congruent, proven by ssa.

First of all, you need to consider that AAA (angle-angle-angle) and SSA (side-side-angle) are not congruence theorems: indeed, you can have two triangles with same angles but sides of different length (it's enough to take a triangle and double all the sides), as it is possible to have two triangles with two sides and one angle not between the two known sides that have the third side of different length.

Second, HL works only for triangles rectangle (for which you have a hypotenuse) and the two triangles of your diagram are not rectangle, therefore you could not use HL.

ASA is a congruence theorem that works when you have two angles and the side between the two known angles. This theorem could be used for your triangles.

Therefore, the correct answer is A) The triangles are congruent, proven by ASA.