Points A and K are marked on the sides of the angle O so that OA = OK. Point B lies inside the angle O

Points A and K are marked on the sides of the angle O so that OA = OK. Point B lies inside the angle O, AB = KB. On the line OB, point D is marked so that B lies between points O and D. Prove that the triangle ADK- isosceles.

Triangles ОАВ and ОВК are equal on three sides, since ОВ is a common side, and ОА = OK and AB = КВ by condition. Then the angle AOB = KOВ, and hence the segment OB is the bisector of the angle AOK and AВK.

Angle ABO = KВO, then the adjacent angles ABD and KBD are also equal.

In triangles ABD and BDK AB = KB, side BD is common, angle ABD = KBD, then triangles ABD and KBD are equal on two sides and the angle between them. Then АD = КD, and consequently, triangle АDК is isosceles, which was required to prove.