For congruent triangles ΔABC and ΔDEF, which of the following statements is…

Concept: Two triangles are congruent when one can be placed exactly on the other by a rigid motion (a slide, turn or flip). By CPCT — corresponding parts of congruent triangles — every pair of corresponding sides is equal in length and every pair of corresponding angles is equal in measure.

The perimeter of a triangle is defined as the sum of its three side lengths, so a side-by-side equality between two triangles forces an equality between their perimeters.

Application — here ΔABC ≅ ΔDEF, so AB = DE, BC = EF and CA = FD:

1. Write the perimeter of the first triangle: P(ABC) = AB + BC + CA.

2. Replace each side by its congruent counterpart in ΔDEF: AB = DE, BC = EF, CA = FD.

3. Substitute: P(ABC) = DE + EF + FD.

4. The right-hand side is exactly the perimeter of ΔDEF, so P(ABC) = P(DEF).

Cross-check and contrast:

• Numerical check: a 3–4–5 triangle congruent to another 3–4–5 triangle gives 3 + 4 + 5 = 12 on both sides, a perimeter ratio of 1 : 1.

• Similar triangles with linear scale factor k satisfy P1 = k × P2. Congruence is the special case k = 1; a ½ × relation would need k = ½, i.e. triangles that are similar but not congruent.

• A strict < or > between the perimeters would need at least one pair of corresponding sides of unequal length, which congruence rules out.

Therefore the correct statement is: Perimeter of ΔABC = Perimeter of ΔDEF.