Rotated triangles can be congruent

To be congruent two triangles must be the same shape and size. However one triangle can be rotated, and as long as they are otherwise identical, the triangles are still congruent. In the figure below, the triangle LMN is congruent to PQR even though it rotated anti-clockwise about 30°

Try this In the figure below, drag any orange dot at P,Q,R and the other triangle will change to remain congruent to it.

Imagine the triangles are cardboard

One way to think about triangle congruence is to imagine they are made of cardboard. They are congruent if you can slide them around, rotate them, and flip them over in various ways so they make a pile where they exactly fit over each other.

In the figure above, if the triangles were cardboard, you could take LMN, turn it slightly clockwise and it would fit exactly over PQR.

Other congruence topics

Congruent Triangles

Congruent Polygons