Question

when constructing a perpendicular bisector why must the compass opening be greater than 1/2 the length of the segment?

Answer 1

Because if the compass opening is lesser than 1/2 the length of the segment, the 2 arcs drawn will never intersect with the segment

Answer 2

While constructing a perpendicular bisector the compass must be opened more than 1/2 the length of the segment:

" Because if we open the compass less than or equal to 1/2 the length then the arcs will never intersect and hence we would never be able to get the perpendicular line "

Explanation:

The construction of a perpendicular bisector of a line segment is as follows:

• Draw a line segment AB.

• Now take a compass and open the span of compass more than half the length of AB.

• Keep compass at A and make a arc below and above the line segment.

• Repeat this process for B.

• Now join the two points where the two arcs intersected.

• The line so obtained is a perpendicular bisector of line and the point where it meets the given line AB is the mid-point of AB.