G is the correct option which is not always true.
In a triangle, if BF is perpendicular to AC, it means that BF is an altitude (height) of the triangle. The perpendicular bisector of AC would be a line that cuts AC into two equal halves and is perpendicular to AC.
Let's analyze the statements:
F. Point F is the midpoint of AC.
If F is equidistant from A and C on line AC, it means F is the midpoint. So, statement F is true.
G. Any point on AC lies on the perpendicular bisector of AC.
This statement is true. Given that F is equidistant from A and C on line AC, F lies on the perpendicular bisector of AC. But this cannot be necessarily true always
H. BF is perpendicular to AC.
This statement is true based on the information given. BF is the perpendicular bisector of AC, and F is equidistant from A and C on AC.
J. Any point on the perpendicular bisector of AC is equidistant from the endpoints of AC.
This statement is true based on the definition of the perpendicular bisector.
Given the information you provided, it seems that all the statements (F, G, H, J) are true. But option G cannot always be true, so G is the correct option.
The probable diagram of the question is attached below.
The probable question would be:
"notice the relationship pattern among the sets of segments drawn from the endpoints of AC to various points of BF.Given the diagram below, which of the following statements is not true
F. Point F is the midpoint of AC.
G. Any point on AC lies on the perpendicular bisector of AC
H. BF is perpendicular to AC
J. Any point on the perpendicular bisector of AC is equidistant from the endpoints of AC"