Which statement is true about proving triangles congruent?

The statement that angle-side-angle (A.S.A.) is a valid method for proving triangles congruent is true because this criterion guarantees congruence between two triangles. When two angles and the included side of one triangle are congruent to the corresponding angles and side of another triangle, it ensures that the triangles are identical in shape and size.

This method is effective because the included side creates a relationship between the two angles, anchoring them together in a way that determines the triangle's overall structure. This congruence criterion comes from the properties of triangles, particularly that the angle measures dictate the length of the sides through the law of sines or can be demonstrated through geometric construction.

Using A.S.A. ensures that both triangles maintain the same shape because the angles dictate the internal configuration and the included side connects those angles, reinforcing the triangle's dimensions. Triangle congruence allows for many applications, such as in proofs and theorems related to geometric figures, making A.S.A. a critical component in triangle congruence discussions.