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If the diagonals of a square ABCD intersect each other at point O, the triangle OAB is :

  1. an equilateral triangle.

  2. a right-angled but not an isosceles triangle.

  3. an isosceles but not a right-angled triangle.

  4. an isosceles right-angled triangle.

Rectilinear Figures

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Answer

In a square,

Diagonals are equal and bisect each other.

If the diagonals of a square ABCD intersect each other at point O, the triangle OAB is : Rectilinear Figures, Concise Mathematics Solutions ICSE Class 9.

∴ AC = BD

⇒ AC2=BD2\dfrac{AC}{2} = \dfrac{BD}{2}

⇒ OA = OB.

Diagonals intersect at right angle.

∴ ∠AOB = 90°.

∴ △ AOB is an isosceles right-angled triangle.

Hence, Option 4 is the correct option.

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