□ ABCD is a parallelogram. Prove that ABD and BDC are similar.

Given ABCD is a ∥gram

To prove : - Δ ABD ∼ Δ BDC

Proof :- For the correspondence ABD ↔ CDB between ΔABD and Δ BDC

∠ BAD ≅ ∠ DCB (opposite ∠s of a ∥gram

∠ABD ≅ ∠CDB (alternate ∠s)

∠ADB ≅ ∠CDB (alternate ∠s)

AB = CD (opposite sides of a ∥ gram ABCD )

∴

Also AD = CB (opposite sides of a ∥ gram ABCD)

∴ = 1

And BD = DB (common)

∴ = 1

Hence, for the correspondence, ABD ↔ CDB between ΔABD and ΔBDC

The corresponding angles are congruent and the lengths of its corresponding sides are in proportion.

∴for the correspondence ABD ↔ CDB, ΔABD and ΔBDC are similar.