(Diagonals of the parallelogram bisect each other) In ΔBCD,P is the mid-point of CD and R is the mid-point of BC. ∴PR||BD (Mid-point theorem) In Δ CQP and Δ COD ∠CQP = ∠COD (Corresponding angles) ∠CPQ = ∠CDO (Corresponding angles) ∴ Δ CQP ~ ΔCOD (AA Similarity) ⇒