Given: AABC with median segments AX, BY, and CZ
Prove: Medians meet at point O.
B
Z
X
It is given that AABC has median segments AX, BY, and CZ. Because
, then AZ = ZB=AY = CY = 1, and
BX CX = The ratios of AZ to ZB is 1, of AY to CY is 1, and of BX to CX is 1 by substitution. Therefore, AAOC, ABOC, and
AAOB are similar to each other. Then the medians meet at point O.
What is the reasoning for the second step?
O A.
OB.
O c.
OD.
medians intersect at one point
medians intersect at multiple points
medians divide each side of the triangle in half
medians divide each side of the triangle into two parts