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Question
Diagonals of rectangle bisect each other at right angles.
Options
True
False
Solution
This statement is True.
Explanation:
⇒ 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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