Using a rule and pair of compass angle 90?

To create a 90 degree angle using a ruler and pair of compass, follow these steps:

1. Draw a straight line using the ruler.
2. Place the compass at one end of the line and draw an arc that intersects the line.
3. Without changing the compass width, place the compass at the other end of the line and draw another arc that intersects the first arc.
4. Draw a straight line connecting the two points where the arcs intersect the original line.
5. The angle formed by the original line and the line connecting the two intersection points is a 90 degree angle.

Materials:

- Ruler
- Compass
- Pencil

Steps:

Step 1: Draw a horizontal line.

Step 2: Open the compass to any convenient radius.

Step 3: Place the compass tip on the line you drew in Step 1.

Step 4: Swing the compass counterclockwise to create a semicircle that intersects the line at two points. Label these points A and B.

Step 5: Reset the compass to a smaller radius than AB.

Step 6: Place the compass tip on point A.

Step 7: Swing the compass to create a small arc that intersects the line above point A. Label this point C.

Step 8: Repeat Step 7 from point B, creating a small arc that intersects the line above point B. Label this point D.

Step 9: Draw a line segment connecting points C and D. This line segment will be perpendicular to the original line and form a 90-degree angle at point O, where it intersects the line.

Note:

- The size of the angle does not depend on the radius of the compass used.
- This method is also known as the Perpendicular Bisector Method.