Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.
using A and B as centers, draw arcs whose radius is greater than 1/2 AB
The line segment connecting the two intersections of the arcs is the desired perpendicular bisector
To create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass, you can follow these steps:
1. Place the compass at point A and draw an arc that intersects the line segment AB on each side. Label the intersections as C and D.
2. Place the compass at point B and draw an arc with the same radius as the previous step. Make sure the arc intersects the line segment AB on each side. Label the intersections as E and F.
3. Without changing the compass width, place the compass at point C and draw an arc that intersects the previous arc at G. Similarly, place the compass at point D and draw an arc that intersects the previous arc at H.
4. Use the straightedge to draw a straight line through points G and H. This line represents the perpendicular bisector to segment AB.
By following these steps, you can create the perpendicular bisector to the segment AB using only an unmarked straightedge and an unmarked compass.
To create the perpendicular bisector of a segment AB using only an unmarked straightedge and an unmarked compass, follow these steps:
Step 1: Place the compass point on point A and draw an arc that intersects segment AB at two points (let's call them C and D).
Step 2: Without changing the compass width, place the point on B and draw two more arcs intersecting segment AB (let's call these points E and F).
Step 3: With the same compass width, place the compass point on C and draw an arc that intersects the previous arc from step 2 (let's call this point G).
Step 4: Keeping the compass width the same, repeat step 3 with the compass point at D, intersecting the previous arc from step 2 (let's call this point H).
Step 5: Using the straightedge, draw a line connecting the points G and H. This line is the perpendicular bisector of segment AB.
Explanation behind the process:
- The first step draws arcs on both sides of segment AB by setting the compass width to a random distance. It doesn't matter what the width is, as long as it remains consistent throughout the process.
- By drawing these arcs from point A, we ensure that they intersect with AB.
- In the second step, the arcs are drawn from point B. The intersecting points E and F should be the same as C and D if the arcs were accurately drawn.
- Points G and H are found by drawing the arcs from C and D, intersecting the previous arcs from step 2 at points E and F.
- Finally, connecting points G and H with a straightedge gives us the perpendicular bisector of segment AB because it divides the segment into two equal halves and is perpendicular to it.