In rectangle ABCD the diagonals meet at point O. a) Prove that triangle AOB is isosceles

In rectangle ABCD the diagonals meet at point O. a) Prove that triangle AOB is isosceles. b) Determine the perimeter of the triangle AOB if it is known that AB = 4 cm, BD = 5 cm

1. If we consider the triangle AOB, it is formed by 1/2 the length of the diagonals AC and BD of the rectangle ABCD, as well as by the side AB. It is known from the properties of the diagonals that they are equal to each other and are halved at the point of intersection. Hence AO is equal to OB and therefore triangle AOB is isosceles.

2. Let’s define its perimeter.

4 + (5/2) * 2 = 9 centimeters.

Answer: 9 centimeters.