Class 9 Mathematics — Chapter 8: Quadrilaterals

1. Consider Diagonal AC (imaginary):
In $\Delta ABC$, $P$ and $Q$ are the midpoints of $AB$ and $BC$. By the **Midpoint Theorem**:
PQ ∥ AC & PQ = ½ AC

2. Opposite side analysis:
In $\Delta ADC$, $S$ and $R$ are the midpoints of $AD$ and $CD$. By the **Midpoint Theorem**:
SR ∥ AC & SR = ½ AC

3. Parallelogram Lock:
Comparing both equations:
PQ ∥ SR & PQ = SR
Since one pair of opposite sides is equal and parallel, **PQRS is a parallelogram**!