Short Answer 
The reflection of triangle XYZ across line MN maintains symmetric properties, ensuring that all corresponding angles and distances, such as angle X’Z’Y’ being equal to 90¬¨‚àû, are preserved. Additionally, line segments like BZ’ and BZ remain equal due to the symmetry of the reflection.
Step 1: Understand the Reflection Concept
In this scenario, triangle XYZ is being reflected across line MN. This line acts as a symmetric axis, meaning that every point on triangle XYZ has a corresponding point on triangle X’Y’Z’. Thus, the angles and distances are preserved during the reflection.
Step 2: Analyze Angles Created by Reflection
Due to the reflective symmetry, we can confirm specific angles between the triangles and the line MN:
- Angle X’Z’Y’ is equal to 90¬¨‚àû since angle XYZ is also 90¬¨‚àû.
- Angle MCY is 90¬¨‚àû because the reflection keeps YY’ aligned with MN.
Step 3: Establish Line Segment Equality
Finally, we conclude that line segments remain equal due to the symmetry of reflection:
- Line segment BZ’ is equal to line segment BZ.
- This equality holds true because the reflection across line MN ensures that corresponding points maintain their distance and alignment.