Question

Prove that the diagonals of a rectangle bisect each other. [4 MARKS]

Answer 1

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

In a rectangle opposite sides are equal and parallel.

In $\Delta OADand\Delta OCB$,

$\angle ODA=\angle OBC$

[Alternate interior angles; $AD\parallel BC$ and BD as transversal]

AD = BC [Opposite sides of a rectangle are equal]

$\angle OAD=\angle OCB$

[Alternate interior angles; $AD\parallel BC$ and AC as transversal]

Hence $\Delta OAD\cong \Delta OCB$ [By ASA congruence rule]

Equating the corresponding parts of congruent triangles, we get:

AO = CO

BO = DO

$\Rightarrow$ Diagonals of a rectangle bisect each other.