In the given figure, ∠AOC = ∠ACO and ∠DBO = ∠BOD. Show that AC || BD.

Given ∠AOC = ∠ACO and ∠DBO = ∠BOD

To prove AC||BD

Proof∠AOC =∠ACO [given]

∠AOC = ∠BOD

[vertically opposite angles]

∠ACO = ∠BOD ,…(i)

∠BOD=∠DBO [given]…(ii) (1)

From Eqs. (i) and (ii), we get

∠ACO =∠DBO

∴ AC || BD [∵ alternate interior angles are equal]