Geometry

Question Analysis:
This question combines the concept of CPCTC with algebraic equations.
The main focus is on using the fact that corresponding sides of congruent triangles are equal to set up and solve an equation.

Key Concept Explanation:
Since △XYZ ≅ △LMN, the corresponding sides are congruent.
So, XY corresponds to LM, and we can set up an equation based on the equality of their lengths.

Step - by - Step Solution:
Given △XYZ ≅ △LMN, so XY = LM.
Substitute the given expressions for XY and LM:
We have the equation 3x - 1 = 2x + 2.
Solve the equation for x:
Subtract 2x from both sides: 3x - 2x - 1 = 2x - 2x + 2.
This simplifies to x - 1 = 2.
Then add 1 to both sides: x - 1 + 1 = 2 + 1.
So, x = 3.

Common Mistakes:
Setting up the equation incorrectly. For example, writing 3x - 1+2x + 2 = 0 instead of 3x - 1 = 2x + 2.
Making errors in solving the algebraic equation, such as incorrect ...