In a convex quadrilateral ABCD, the angles ACD = ABD. Prove that the angles ACB = ADB.

In this task, we will prove the equality of the given angles;

To do this, consider our quadrilateral;

Since the quadrilateral is convex, according to the condition of the assignment, it means the angles BOA = DOC, as opposite angles when two straight lines are crossed;

It follows that triangle ABO and triangle CDO are similar, in two angles, and hence the angle BAO = CDO, as well as their sides of the wound to the ratio AB / CD = AO / CO = BO / DO;

Now consider the triangle BOC and AOD;

The angles AOD = BOC, as opposite angles when crossing two straight lines, which means that the triangles AOD and BOC are similar and therefore the angle ACB = ADB.