Final answer:
Given that triangle APQR is a right triangle and it is congruent to triangle AXYZ, AXYZ must also be a right triangle. Congruency implies all corresponding sides and angles are equal, preserving all properties of the triangle including angles.
Step-by-step explanation:
The question asks whether triangle AXYZ has to be a right triangle given that triangle APQR is a right triangle and that APQR is congruent to AXYZ. In geometry, when two triangles are congruent (APQR - AXYZ), it means that they are identical in shape and size, having all corresponding sides and angles equal.
The fact that APQR is a right triangle implies one of its angles is 90 degrees. Since AXYZ is congruent to APQR, each angle in AXYZ will match its corresponding angle in APQR. Therefore, AXYZ must also have a 90-degree angle, making it a right triangle as well. This is because congruency preserves all the properties of a triangle, including the type of angles it contains.
For example, if in triangle APQR, angle P is the right angle, then in triangle AXYZ, the angle that corresponds to angle P will also be a right angle. This is a principle foundational to congruent triangles in Euclidean geometry.