Complete the following proof.

BD = CA ⇒ Proved down

Step-by-step explanation:

From the given figure

∵ AB and CD are diameters in circle O

∴ OB = OA = OC = OD ⇒ radii

∵ AB ∩ CD at O

∴ ∠BOD and ∠COA are vertically opposite angles

∵ The vertically opposite angles are equal in measures

∴ m∠BOD = m∠COA

→ In Δ OBD and Δ OCA

∵ m∠BOD = m∠COA ⇒ vertically opposite angles

∵ OB = OC ⇒ radii

∵ OD = OA ⇒ radii

∴ Δ OBD and Δ OCA are congruent by SAS postulate

→ From congruency

∴ BD = CA