The diagonals of rectangle ABCD intersect at point O and form an angle AOD equal to 120

The diagonals of rectangle ABCD intersect at point O and form an angle AOD equal to 120 degrees. Determine the type of triangle AOB.

1. It is known that the diagonals of the rectangle are equal and the intersection point is halved;

the sum of the angles of the triangle is 180 degrees;

the sum of adjacent angles is 180 degrees.

2. The angle AOB is adjacent to the angle AOD, which by condition is equal to 120 degrees, so the angle AOB = 180 degrees – 120 degrees = 60 degrees.

3. We found out that AO = OB, so the triangle AOB is isosceles.

The AOB angle is 60 degrees, which means

angle AOB + angle ABO = 180 – 60 = 120 degrees, but in an isosceles triangle the angles at the base are equal

angle AOB = angle ABO = 120: 2 = 60 degrees.

We got a triangle in which all angles are equal, which means that the AOB triangle is equilateral.

Answer: The AOB triangle is equilateral.