This picture proof shows how vertically opposite angles of two intersecting lines are congruent. This picture proof helps show that even when the lines are moved within the distance between the two points on each line, the vertically opposite angles will always be equal. The two lines that are intersecting each other are not perpendicular to one another, they just cross each other at a point. The intersection point must stay within the points on the line that are created because if the intersection point goes outside of the points, they will not be equal anymore (because the angles were measured with these points).

As can be seen from the picture proof created, the lines can be moved to any position, and as long as the intersection stays between the points on the lines, the angles stay the same (the angles will not stay the same when outside of the points of one of the lines because the angles were measured with those points, changing the orientation of the angle). The angles opposite of each other were always equal, showing that vertically opposite angles are always congruent.