Given the triangles NSQ and NPQ, you need to remember that two triangles are congruent if their corresponding sides are equal and if their corresponding angles have the same measure.
In this case, you can identify that:
- Sides NS and PQ have the same indicator mark. That indicates that they are equal.
- Angles S and P have the same indicator mark. That indicates that they have the same measure.
- Both triangles have the side NQ in common.
According to one of the Congruence Theorems for Triangles called Side-Angle-Side (SAS), if the included angle and the two included sides of two triangles are equal, the triangles are congruent.
In this case, you know that both sides have two equal corresponding sides. But since the angle is not formed by the included sides that are equal, you cannot apply the SAS rule to prove they are congruent. You do not have enough data to prove they are congruent.
Hence, the answer is: These triangles cannot be proven congruent.