In a rectangle ABCD, the diagonals bisect at O. What kind of a triangle AOB is?


Answer:

an isosceles but not right angled triangle

Step by Step Explanation:
  1. Following figure shows the rectangle ABCD with diagonals.
  2. We know that diagonals of a rectangle are equal and bisects each other, therefore
      AC = BD
    ⇒ AC/2 = BD/2
    ⇒ AO = OB

    Also, ∠AOC ≠ 90° .... (since diagonals are not perpendicular)
  3. Since AO = OB and ∠AOC ≠ 90° , triangle ΔAOB is an isosceles but not right angled triangle.

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