In the figure to the right point o is the midpoint of segment ab . through point o is drawn a line ox .perpendicular to ab . prove that any point on line ox is equidistant from a and b.

See proof below

Step-by-step explanation:

Point O is the midpoint of segment AB. Through point O is drawn a line OX perpendicular to AB. Consider two triangles AOX and BOX. These triangles are right triangles, because OX is perpendicular to AB. In these triangles:

Thus, by LL theorem.

Congruent triangles have congruent corresponding sides, then AX=BX. This means that point X is equidistant from points A and B.