With the help of compass and ruler construct an angle of measure 90 degree, and bisect it.
Answers
Answer: Through the Middle of a Line Segment
1
Draw a straight line. On a piece of paper, draw a line segment of any convenient length. Make it horizontal for the sake of simplicity, but it could be at any angle. Label the line segment AB.
2
Pick any point on AB. Mark it, and label it O. O can be anywhere on the line segment, including at either endpoint (A or B). For convenience, let's put O somewhere near the middle of AB. The line segment could now be referred to as AOB.
3
Grab a compass. Open the compass to a radius a little shorter than either AO or OB. Now place the compass point at O. Strike short arcs through AB on either side of O. The two arcs should have the same radius. Label those two points of intersection C and D. Now the line segment could be referred to as ACODB.[5]
4
Strike two more arcs. Place the compass point at C, and strike an arc to one side of the line segment. Then place the compass point at D, and strike a second arc of the same radius and on the same side of the line segment. Make sure those two arcs intersect. Call that point of intersection E.
5
Draw the 90° angle. Draw a straight line from E to O. Line segment EO forms a 90° angle with line segment AB. It actually forms two 90° angles at O. If you were to extend EO beyond AB, you would form four 90° angles at O.[6]
Note that you can draw a 90° angle at either end of line segment AB if you want to (in other words at point A or point B). Simply extend AB beyond A or beyond B, and then follow the above steps. Point A (or point B) would serve as point O in the above instructions.
This is essentially the same method featured in How to Construct a Perpendicular Line to a Given Line Through Point on the Line
