Question

two ropes are tied to the same place on a tree growing perpendicular to the ground. each rope is anchored to the ground the same distance from the base of the tree. which statement is true because of the perpendicular bisector theorem? a. the length of rope between where it is tied to the tree to where it is anchored to the ground is the same for both ropes. b. for each anchor, the length of the rope between the anchor and where the rope is tied to the tree is the same as the distance between the anchor and the base of the tree. c. the height at which the ropes are tied to the tree is the same distance as the length between the two anchors. d. the ropes form right angles where they are anchored to the ground.

Explanation:

The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. In this case, the tree is perpendicular to the ground (acting as a perpendicular bisector of the segment connecting the two anchors). The ropes are the segments from the point on the tree (a point on the perpendicular bisector) to the anchors (endpoints of the segment on the ground). So, by the perpendicular bisector theorem, the lengths of the two ropes (from tree - tie point to anchors) are equal.

Answer:

A. The length of rope between where it is tied to the tree to where it is anchored to the ground is the same for both ropes.