Question

Triangles K L P and Q M N are shown. Triangle Q M N is slightly higher than triangle K L P and side Q M connects to side K P. Point M is at the midpoint of K P. Sides K L and Q N are congruent. Angles K L P and Q N M are congruent. Angles K P L and Q M N are both right angles.
Is there a series of rigid transformations that could map TriangleKLP to TriangleQNM? If so, which transformations?

No, TriangleKLP and TriangleQNM are congruent but TriangleKLP cannot be mapped to TriangleQNM using a series rigid transformations.
No, TriangleKLP and TriangleQNM are not congruent.
Yes, TriangleKLP can be reflected across the line containing KP and then translated so that P is mapped to M.
Yes, TriangleKLP can be rotated about P and then translated so that L is mapped to N.

Answer 1

Yes. Rotate triangle KLP about P to line up PL with MN (and PK with MQ), then translate so P goes to M. This rotation + translation (a rigid motion) maps K→Q, L→N, P→M.