Q how to bisect an angle?
I assume you mean with a compass and straightedge (ruler).
Refer to the figure at
http://etc.usf.edu/clipart/32400/32417/_32417_lg.gif
Put the point of the compass at the vertex (B in the figure) and draw arc 1 through both sides of the angle. Then, using a shorter fixed radius for the compass, and putting he point of the compass at the places where arc 1 interects the sides of the angle, draw arcs 2 and 3 so that they intersect.
Then draw the line through the vertex and the points where arcs 2 and 3 intersect. It will bisect the angle.
To bisect an angle means to divide it into two equal parts. There are different methods to bisect an angle, but I'll explain one common geometrical method called the "angle bisection construction."
Here are the steps to bisect an angle using the angle bisection construction:
1. Draw the angle you want to bisect. Let's call the two arms of the angle "line AB" and "line AC."
2. With the center at point A, draw an arc that intersects both line AB and line AC. This will create two points on the arc: point M and point N.
3. From points M and N, draw straight lines that intersect each other. Let's call this point of intersection "point O."
4. Now, draw a straight line from point O to point A.
5. The line AO will bisect the angle, dividing it into two equal parts. You can verify this by measuring the angles formed by line AO and line AB, as well as line AO and line AC.
It's important to note that this is just one method to bisect an angle. There are other advanced methods involving compass and straightedge constructions, as well as more intricate geometric techniques.