To find the values of x and y, we can set up an equation based on the given information. Since triangles ABC and DEF are congruent, their corresponding sides are equal in length.
From the given information, we have:
AB = 11
AC = 17 + x
DF = 2x + 13
DE = 3y + 2
Since AB and DE are corresponding sides, we can equate them:
11 = 3y + 2
Solving this equation, we find:
3y = 11 - 2
3y = 9
y = 3
Now, using the fact that AC and DF are corresponding sides, we can equate them:
17 + x = 2x + 13
Solving this equation, we find:
x - 2x = 13 - 17
-x = -4
x = 4
Therefore, x = 4 and y = 3.