Properties: 1 Mark
Proof: 1 Mark
Steps: 2 Marks

In a rectangle opposite sides are equal and parallel.
In $\mathrm{Δ}OAD\text{Â}and\text{Â}\mathrm{Δ}OCB$,
$\mathrm{âˆ}ODA=\mathrm{âˆ}OBC$
[Alternate interior angles; $ADâˆ\yen BC$ and BD as transversal]
AD = BC  [Opposite sides of a rectangle are equal]
$\mathrm{âˆ}OAD=\mathrm{âˆ}OCB$  
[Alternate interior angles; $ADâˆ\yen BC$ and AC as transversal]
Hence $\mathrm{Δ}OADâ‰\dots \mathrm{Δ}OCB$   [By ASA congruence rule]
Equating the corresponding parts of congruent triangles, we get:
AO = CO
BO = DO
$⇒$  Diagonals of a rectangle bisect each other.