To solve the problem in the image, let's analyze the triangles and the questions.

Part (a): Identifying the Congruency Test

The triangles are given with one pair of corresponding sides marked as equal (7.4 and 12.1), and there is also an indication that the angle between these sides is the same (since both triangles share a marked angle).

Given that two sides and the included angle are congruent, the correct congruence test to prove the triangles are congruent is SAS (Side-Angle-Side).

Part (b): Finding the Value of "a"

Since the triangles are congruent by the SAS test, their corresponding sides must be equal. Therefore, to find the value of $a$, you can equate the corresponding sides from the congruent triangles.

The corresponding side to $a$ in the other triangle is 12.1, so: $a = 12.1$

Thus, the value of $a$ is 12.1.

Would you like more details on these solutions or have any additional questions?

Here are five related questions you might find helpful:

1. How does the SSA congruence test differ from SAS?
2. Why is the angle between the sides important for the SAS test?
3. What would happen if the given angle was not between the two sides?
4. How can you prove triangle congruence using the AAS (Angle-Angle-Side) method?
5. How do you determine the corresponding sides and angles in congruent triangles?

Tip: When dealing with triangle congruence, always check the position of the angle relative to the sides being considered.