The ancient Greeks required a straightedge and protractor to construct a perpendicular bisector for a given line segment.A.TrueB.False

The statement is False.

Explanation:

In ancient Greek geometry, a perpendicular bisector can be constructed using only a compass and a straightedge. The method involves the following steps:

1. Identify the Line Segment: Let’s say we have a line segment $AB$.

2. Construct Arcs: Using the compass, place the point on point $A$ and draw an arc above and below the line segment. The radius of the arc should be more than half the length of $AB$.

3. Repeat from Point B: Without changing the compass width, place the compass on point $B$ and draw similar arcs that intersect the previous arcs.

4. Connecting Intersections: The two arcs from points $A$ and $B$ will intersect at two points. Connect these intersection points with a straightedge. This line is the perpendicular bisector of the segment $AB$.

Thus, the construction does not require a protractor. Therefore, the statement is false.