Answer :
Final answer:
If point P is on line segment AB, then the statement that is always true is b) PB > AP.
Explanation:
When point P lies on the line segment AB, it divides the segment into two parts: AP (the portion from point A to P) and PB (the portion from point P to B). Since P lies on the segment AB, PB represents the remaining part of the segment after removing AP. As a result, PB is always longer than AP, making option **b) PB > AP** the correct choice.
When we place point P closer to point B, PB increases while AP decreases, but PB will always be greater than AP due to their positions relative to point P. Even if we move point P to coincide with point A or point B, the lengths of AP and PB become zero, and in this case, PB is still greater than AP, adhering to the statement in option b.
In contrast, options a) AP > PB and c) AB > AP are not necessarily true. Depending on the specific positioning of point P along line segment AB, these statements can be false. Option d) AB > AP + PB is also not always true, as it implies that the sum of AP and PB is smaller than AB, which isn't necessarily the case.
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