describe a process you would use to create the perpendicular bisector to a segment a b using only an unmarked straight edge and an unmarked compass
To create a perpendicular bisector to a segment AB using only an unmarked straightedge and compass, you can follow the following steps:
1. Place the compass needle at point A and draw an arc that intersects the segment AB on both sides. Make sure to keep the compass open to a reasonable distance that can create two visible intersections, but not too wide.
2. Without adjusting the compass size, place the compass needle at point B and draw another arc that intersects the segment AB on both sides. The arcs should intersect with the previous arcs you drew in step 1.
3. Using the straight edge, draw lines connecting the points where the arcs intersected on both sides of the segment AB. Let's call those points C and D respectively.
4. Finally, use the straightedge to draw a line passing through points C and D. This line will be the perpendicular bisector of the segment AB, dividing it into two equal halves.
It is important to note that the accuracy of this method strongly relies on maintaining the same compass size throughout the process and ensuring the arcs intersect the segment AB on both sides.
To create the perpendicular bisector of segment AB using only an unmarked straight edge and an unmarked compass, follow these steps:
1. Place your compass point on point A and draw an arc that intersects segment AB on both sides.
2. Without changing the compass width, place the compass point on point B and draw another arc that intersects segment AB on both sides.
3. Draw straight lines connecting the points where the arcs intersect segment AB, creating two line segments.
4. Use your straight edge to connect the two points where the arc intersects segment AB, creating a line that extends beyond segment AB.
5. Place your compass point on one of the points where the arc intersects the line you just drew and set the compass width to a distance greater than half the length of segment AB.
6. Without changing the compass width, draw an arc that intersects the line at two points.
7. Repeat step 6, this time placing the compass point on the other point where the arc intersects the line.
8. Use your straight edge to draw a line connecting the two points where the new arcs intersect.
9. The line you just drew is the perpendicular bisector of segment AB.
Remember, when using this process, keep the compass width the same throughout and ensure that you mark the arcs and lines accurately.
To create the perpendicular bisector of a segment AB using only an unmarked straight edge and an unmarked compass, follow these steps:
1. Start by placing the compass point on point A and extending the compass to point B. Make sure to maintain this distance throughout the process.
2. Draw two arcs, one above and one below the line AB, intersecting the line on both sides. These arcs should be large enough to intersect the line on both sides.
3. Without changing the compass width, place the compass point on point B and draw two more arcs, intersecting the line again on both sides.
4. Using the straight edge, draw a line connecting the points where the intersecting arcs meet. This line should pass through the mid-point of segment AB.
5. The line you just drew is the perpendicular bisector of segment AB.
Explanation:
The process described above follows the construction principle of a perpendicular bisector. By drawing arcs with the same compass width above and below the segment AB, we are finding points equidistant from both ends of the segment. By drawing arcs intersecting the line from both ends of the segment, we are again finding points equidistant from both ends, but this time on the other side of the segment. Connecting the points where these arcs intersect gives us the perpendicular bisector, as it passes through the mid-point of the segment and creates right angles with all points on the segment.