Geometry

Question Analysis:
This question combines:
AAS congruence conditions
Algebraic equation solving
Length calculation precision
The main focus is on:
Establishing the correct equation for congruence
Solving for the unknown variable

Key Concept Explanation:
For AAS congruence:
Required congruent parts:
∠A ≅ ∠D (given)
∠B ≅ ∠E (given)
BC ≅ EF (non-included sides)
Therefore, set BC = EF

Step-by-Step Solution:
List Given Information:
∠A ≅ ∠D
∠B ≅ ∠E
BC = 2x + 1
EF = x + 5
Apply AAS Condition:
Required congruent sides: BC ≅ EF
Equation: 2x + 1 = x + 5
Solve for x:
2x - x = 5 - 1
x ...