Given a trapezoid OKMN (ON- larger base). The sides of the trapezoid are extended to the intersection

Given a trapezoid OKMN (ON- larger base). The sides of the trapezoid are extended to the intersection at point S. Prove that the triangle SON is similar to the triangle SKM.

Since OKMN is a trapezoid, the base ОN is parallel to the base of the CM.

Then the angle SON is equal to the angle SKM, and the angle SNO is equal to the angle SMK as the corresponding angles at the intersection of parallel straight lines ON and KM with secants SO and SN.

Then in triangles SON and SKM two angles at the bases are equal, then these triangles are similar in the first sign of similarity of triangles, in two angles, which was required to prove.