AB and CD are equal chords of a circle centered on O. Prove that triangle ABO = triangle CDO.

From the point O of the center of the circle, we construct the radii OA, OB, OC, OD.

Since, according to the condition, the chords AB and CD are equal, the arc AB is equal to the arc CD, and then the central angle AOB = COD since they are based on equal arcs.

Then in the triangles ABO and CDO, the angle AOB = BOC, OA = OB = OC = OD = R, and then the triangles are equal in two sides and the angle between them, which was required to prove.