Geometry

Question Analysis:
This question involves using algebra and geometric properties together.
The main focus is applying the condition that one pair of opposite sides being both parallel and congruent proves a parallelogram.

Key Concept Explanation:
If one pair of opposite sides are both parallel (given as AB // CD) and congruent, then the figure is a parallelogram.
So, we must set the two sides equal:
AB = CD → 2x + 3 = 5x − 9

Step-by-Step Solution:
Set the expressions equal:
2x + 3 = 5x − 9
Solve for x:
Subtract 2x from both sides: 3 = 3x − 9
Add 9 to both sides: 12 = 3x
Divide by 3: x = 4

Common Mistakes:
Solving the ...