• 1. Draw a segment and create a perpendicular bisector using the geometric construction techniques.
• 2. Draw an angle and create an angle bisector using geometric construction techniques.
To draw a segment and create a perpendicular bisector, follow these steps:
1. Start by drawing a line segment AB of any desired length.
2. Place the point of the compass on point A and draw an arc that intersects the line segment at two points.
3. Without changing the compass's width, place the point on point B and draw another arc that intersects the line segment at two points.
4. Use a straight edge or ruler to connect the intersection points of the two arcs. This line should pass through the midpoint of segment AB.
5. The line you just drew is the perpendicular bisector of segment AB, dividing it into two equal halves.
To draw an angle and create an angle bisector, follow these steps:
1. Start by drawing a ray AB. The starting point A will be the vertex of the angle you want to bisect.
2. With point A as the center, draw an arc that intersects both sides of the angle.
3. Use a compass to find the same distance on each side of the angle's vertex, and draw arcs from the intersections with the sides of the angle.
4. Connect the vertex of the angle to the point where the arcs intersect. This line will be the angle bisector, dividing the angle into two equal halves.
Remember, geometric constructions are done with the help of only a compass and a straight edge, without any measurements or calculations.
You have a compass?
Set its width at about 3/4 the length of the line segment.
put the point of the compass at one end of the segment and draw a circle
put the point of the compass at the other end and draw a circle.
those circles intersect on each side of the segment.
draw a line between the two intersections to the circles.
Now prove that it is the perpendicular bisector :)
Use that compass again.
It is so close to what we just did that I am going to let you figure it out now.
bisect angle with compass and straightedge:
http://www.youtube.com/watch?v=tDXrY8E3bFs