Line OM parallel to the lateral side AC of triangle ABC meets sides AB and BC at points O

Line OM parallel to the lateral side AC of triangle ABC meets sides AB and BC at points O and M. prove that triangle BOM is isosceles

In this task, it is necessary to prove that the resulting triangle is isosceles;

To do this, we will perform the construction and consider it;

Since the straight line OM is parallel to the side of the isosceles triangle AC, then the angles of the small triangle BAC and BCA are equal to the angles of the larger triangle PTO and BMO, respectively;

From the property of an isosceles triangle, we know that the angles at the base of an isosceles triangle are equal, and vice versa, if the angles are equal, then the triangle is isosceles;

Therefore, the PTO angle = BMO, and hence the PTO triangle is isosceles.