In rectangle ABCD, the diagonals meet at point O; angle COD = 60 degrees, CD = 10 cm. What are the diagonals of the rectangle?

1. The diagonals of the rectangle are equal to each other and are halved at the point of intersection.

Therefore, the triangle COD is isosceles. This means that the angles at the base of the CD of this triangle are equal. We calculate their value:

Angle DСО = angle ОDС = (180 ° – 60 °) / 2 = 60 °.

2. The three angles of the triangle are equal. Therefore, the triangle COD is equilateral.

OC = CD = DO = 10 centimeters.

3. Calculate the length of the diagonals:

AC = BD = 10 x 2 = 20 centimeters.

The length of each diagonal of the rectangle ABCD is 20 centimeters.