Using the perpendicular bisector theorem, statement D. "The length of ropes between where it is tied to the tree to where it is anchored to the ground is the same for both ropes".
What is perpendicular bisector theorem?
The perpendicular bisector theorem states that any point on the perpendicular bisector is equidistant from both the endpoints of the line segment on which it is drawn.
In this question, there is only one point on the perpendicular bisector which is connected to the line segment on which it is drawn, it is the point on which the rope is tied to the tree. Thus, using perpendicular bisector theorem, the point at which rope is tied to the tree is equidistant to the end points of the line segment on which perpendicular is drawn, which is also the point on the ground from where the ropes are anchored.
This proves that the length of ropes between where it is tied to the tree to where it is anchored to the ground is the same for both ropes.
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