When constructing a perpendicular bisector, why must the compass opening be greater than one half the length of the segment
Oh come on cassie. Try it!
If the opening does not reach halfway, no way you can swing it off to the side and get the swings from both ends to intersect!
Try is with a line segment on your desk and use your fingers for a compass.
When constructing a perpendicular bisector of a line segment, the compass opening must be greater than one-half the length of the segment. This is because the perpendicular bisector is a line that cuts the original segment into two equal halves, forming a 90-degree angle with it.
To understand why the compass opening needs to be greater than one-half the length of the segment, let's go through the steps of constructing a perpendicular bisector:
1. Place the compass on one end of the line segment and adjust the opening to be greater than half its length.
2. Draw two arcs on either side of the segment that intersect it.
3. Without changing the compass opening, place the compass on the other end of the segment and repeat step 2.
4. Draw a straight line that intersects the two arcs.
5. The line you drew in step 4 is the perpendicular bisector of the line segment.
The reason the compass opening needs to be greater than half the length of the segment is to ensure that the intersecting arcs are wide enough to intersect each other. If the opening is too small, the arcs may not intersect, resulting in an inaccurate perpendicular bisector.
By having the compass opening greater than half the length of the segment, we ensure that the intersecting arcs will be wider and will definitely intersect each other. This guarantees the accuracy of the construction and the correct formation of the perpendicular bisector.
So, it's essential to use a compass opening greater than one-half the length of the segment when constructing a perpendicular bisector to ensure an accurate and precise result.