To determine which rigid transformation maps Triangle MZK to Triangle QZK, let's analyze the given information:
- Sharing Side: Triangles MZK and QZK share the side ZK.
- Congruent Angles: Angles MKZ and ZKQ are congruent.
- Right Angles: Angles KZM and KZQ are both right angles.
With both triangles sharing side ZK and having congruent angles, we can establish the following:
- Since angles KZM and KZQ are right angles, angle MZK will be oriented vertically with respect to side ZK in triangle MZK, while triangle QZK will have angle QZK also oriented vertically.
- The congruence of angles MKZ and ZKQ suggests that the triangles can be perfectly aligned based on the angles.
This situation describes a transformation where one triangle can be flipped or reflected over some line of symmetry to align with the other triangle.
Let's analyze the options for rigid transformations:
- Rotation about point K: This wouldn’t align the two triangles because the angles and sides would not match due to the different positions of M and Q.
- Reflection across the line containing MZ: This wouldn’t apply because it wouldn’t align QZK with MZK.
- Reflection across the line containing ZK: This is the most appropriate option since reflecting Triangle MZK across line ZK would align point M with point Q, preserving angles and side length.
- Rotation about point Z: Similar to the rotation about point K, this wouldn't correctly align the triangles because rotation would shift points rather than mirror them across the line ZK.
Thus, the correct answer is:
a reflection across the line containing ZK.