Geometry

Question Analysis:
This question involves understanding the properties of congruent triangles and how congruency affects perimeter.
The main focus is on the relationship between corresponding sides in congruent triangles and their effect on perimeter.

Key Concept Explanation:
Two triangles are congruent if and only if their corresponding sides and corresponding angles are equal.
This means:
Each pair of corresponding sides in the two triangles is equal.
Since perimeter is the sum of all three side lengths, the perimeters of both triangles must also be equal.

Step-by-Step Solution:
Understand the given information:
We are told that △ABC ≅ △XYZ.
This means that AB = XY, BC = YZ, and AC = XZ.
Calculate the perimeters of both triangles:
Perimeter of △ABC = AB + BC + AC
Perimeter of △XYZ = XY + YZ + XZ
Since corresponding sides are equal:
AB = XY, BC = YZ, AC = XZ
Substituting these into the perimeter equation:
AB + BC + AC = XY + YZ + XZ
Conclusion:
Since the sum of the side lengths is the same, the perimeters must be equal.

Common Mistakes:
Confusing congruency with similarity:
Some students mistake congruent triangles (equal sides, equal perimeters) for similar triangles (proportional sides,...