Geometry

Question Analysis:
This question combines CPCTC with the concept of triangle perimeter.
The main focus is on using the perimeter formula and the property of corresponding sides of congruent triangles.

Key Concept Explanation:
First, we know that the perimeter of a triangle is the sum of its side lengths.
For △ABC, Perimeter = AB + BC+ AC.
Also, since △ABC ≅ △DEF, corresponding sides are equal, so AB = DE, BC = EF, and AC = DF.

Step - by - Step Solution:
Calculate the length of AC in △ABC.
Given the perimeter of △ABC = 24 cm, AB = 7 cm, and BC = 9 cm.
Using the perimeter formula P = AB + BC + AC, we can find AC.
Substitute the values: 24 = 7 + 9+ AC.
Simplify the right - hand side: 24 = 16 + AC.
Subtract 16 from both sides to get AC = 24 - 16 = 8 cm.
Apply CPCTC.
Since △ABC ≅ △DEF, and AC corresponds to DF, then DF = AC.
Since AC = 8 cm, DF = 8 cm.

Option Analysis:
Option A: AB = 7 cm, but DF does not correspond to AB, so this option is incorrect.
Option B: DF = 8 cm as calculated above, so this option is correct.
Option C: BC = 9 cm, and DF does not correspond to BC, so this option is incorrect.
Option D:...