The correct option is  i.e., AAS.
 i.e., AAS.
Further explanation:
Given that two angles of one triangle and the non-included side are congruent to the corresponding parts of another triangle.
ASA congruence rule:
If two angles and the included side of one triangle are congruent to two angles and the included side of other triangle, then both the triangles are congruent from the Angle-Side-Angle axiom of congruence.
Consider two triangles as  and
 and  as shown in Figure 1.
 as shown in Figure 1.
Now, assume that  and
 and  are equal and the side AC bisects
 are equal and the side AC bisects  as shown in Figure 1.
 as shown in Figure 1.
The side AC is common to both the triangles.
The sum of three angles of a triangle is equal to  .
.
The  is calculated as  follows:
 is calculated as  follows:

The  is calculated as  follows:
 is calculated as  follows:

The  is equal to
 is equal to  and
 and  is equal to
 is equal to  .
.
Then the  is  calculted as follows:
 is  calculted as follows:

Therefore, all the three angles of the  are equal to corresponding angles of
 are equal to corresponding angles of  .
.
If all the angles of triangle are equal to corresponding angles of another triangle, then it is not necessary that the triangles are congruent.  
So for triangles to be congruent from three equal parts there should be one side.
Thus, AAS congruence theorem can be used to prove that the triangles are congruent.
Therefore, the correct option is  i.e., AAS.
 i.e., AAS.
Learn more:
1. Problem about triangles brainly.com/question/7437053
2. The product of a binomial and a trinomial is x 3 + 3 x 2 − x + 2 x 2 + 6 x − 3. Which expression is equivalent to this product after it has been fully simplified? brainly.com/question/1394854
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Triangles
Keywords:
Triangles, congruence, two angles, one side, AAS, theorem, ASA, SSS, SAS, HL, prove, non-included side.