To identify if two triangles are congruent, we have three postulates and two theorems to help us. They are called.
AAS Theorem (Angle-Angle-Side Theorem) - it is said that 2 traingles are congruent if the 2 triangles has 2 congruent ANGLES and 1 congruent SIDE.
HL Theorem (Hypothenuse-Leg Theorem) - it is said that 2 triangles are congruent if the hypothenuse and a leg of 2 right triangle are congruent.
SSS Postulate (Side-Side-Side Postulate) - it is said that 2 triangles are congruent if all of the sides of the 2 triangles are congruent.
ASA Postulate (Angle-Side-Angle Postulate) - it is said that 2 triangles are congruent if the 2 angles and the side between them of 2 triangles are conguent.
SAS Postulate (Side-Angle-Side Postulate) - it is said that 2 triangles are congruent if the 2 sides and the angle between them of the 2 triangles are congruent.
So based on the definitions above we can already rule out the LETTER A, LETTER C. and LETTER E since there is no LL, HA, and AAS theorem or postulate.
Now we are left with 3 possible answers. Namely SAS, ASA, HL.
Looking at the picture SAS postulate is imposible since there are only 1 SIDE of the 2 traingles which is indicated as congruent.
So that leaves us with 2 remaining possible answer. We can also see that the HL theorem is also impossible since even though our triangle is a right triangle it only indicated that only the hypothenuse are congruent and there are no indicator of 2 congruent leg.
So that gives us the remaining choice of ASA. In which we can see that 2 angles of the 2 traignle is congruent so as the Side in between the two angles. Therefore we can use the ASA postulate to prove that the 2 triangles are congruent.
Meaning only LETTER D. is the one that should be checked because it is the only one which we can give as the reason why the 2 traingles are congruent.