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Geometry Sem 1
5.1.3 Quiz: Proving Theorems about Triangles: Mastery Test
Question 5 of 5
Given: AABC with median segments AX, BY, and cz
Prove: Medians meet at point O.
B
X
с
It is given that AABC has median segments AX, BY, and cz.
Because
then AZ = ZB = 1, 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, ▲AOс,
ABOс, and AAOв are similar to each other. Then the
medians meet at point O.
What is the reasoning for the second step?