Given:
with median segments
,
, and

Prove: Medians meet at point O.

The picture shows a triangle ABC with a center O. A-line AX is drawn perpendicular to BC, CZ is drawn perpendicular to AB, and BY is drawn perpendicular to AC.

It is given that
has median segments
,
, and
. Because ___________, then
,
, and
. The ratios of
to
is 1, of
to
is 1, and of
to
is 1 by substitution. Therefore,
,
, and
are similar to each other. Then the medians meet at point O.

What is the reasoning for the second step?

A.
medians intersect at one point
B.
medians divide each side of the triangle into two parts
C.
medians divide each side of the triangle in half
D.
medians intersect at multiple points