Q112 of 160 Page 144

State whether the statements are true (T) or false (F).

Diagonals of a rectangle bisect each other at right angles.

TRUE


In rectangle ABCD, diagonals bisect the angles.
Consider ΔAOD and ΔBOC
AD = BC (ABCD is a rectangle)
∠AOD = ∠BOC (Vertically opposite angles)
∠OAD = ∠OCB = 45° (Diagonals bisect the angles)
ΔAOD ≅ ΔBOC (AAS congruence criterion)
Therefore, OA = OC and OB = OD
Thus the diagonals bisect each other in a rectangle.


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