If the corresponding angles of two triangles are equal then they are always congruent. The Given statement( a ) is always true( b ) is always false( c ) can be true( d ) can be determined

The given statement says, "If the corresponding angles of two triangles are equal, then they are always congruent."

Let's analyze this:

Corresponding Angles: If two triangles have their corresponding angles equal, it implies that both triangles share the same angle measures at the respective positions.

Congruent Triangles: Two triangles are said to be congruent if their corresponding sides and angles are equal.

In geometry, the rule known as the Angle-Angle-Angle (AAA) similarity criterion states that if two triangles have equal corresponding angles, they are similar, meaning their shape is the same, but not necessarily their size. However, AAA similarity does not imply congruency because congruency requires both equal angles and equal side lengths.

Therefore, while equal corresponding angles imply that the triangles are similar, they do not guarantee that the triangles are congruent unless the corresponding sides are also equal.

The correct answer is:
(c) can be true