Here is exactly how to construct a square making use of a straightedge, a compass, and of course a pen or a pencil.

You are watching: How to construct a square with a compass and straightedge

Step 1

Draw a segment and call it AB.


Step 2

Construct a line perpendicular to segment ab and let ns be the point where the perpendicular line intersects segment AB. Evaluation the lesson around constructing perpendiculars if needed. 


Step 3

Set your compass come the size of IB. Then, copy segment IB onto the perpendicular heat (shown with the blue line). Brand the brand-new point top top the perpendicular line C.


Step 4

Set your compass again to the length of IB and also draw arcs from point C and from point B. Label the point of intersection between the two brand-new arcs D.


Step 5

Using a straightedge, attract segment CD and also segment BD. You have actually just built the square ICDB presented with 3 blue segments and 1 black segment.


How to construct a square : an approach #2 

Step #1: Using a straightedge, attract a segment abdominal muscle with a size of her choice.

Step #2: Using a compass, measure the size of segment AB. Maintaining the opened of your compass the same, placed the needle that the compass at point A and also draw a circle. The length of the radius the the circle will certainly be same to the size of segment AB. 

Then, still keeping the opening of your compass the same, placed the needle the the compass at allude B and draw another circle. After ~ you room done illustration both circles, you should end up through the number below. Finally, brand the allude where the two circles meet I. 

Step #5: Still using the same compass opening in action #4, put the needle that the compass in ~ I and also draw a little arc. Label the arc K. Then, still making use of the same compass opened in step #4, placed the needle the the compass at point J and also draw a tiny arc. Brand the arc F.

Step #6: Finally, connect the clues I, J, F, and also K. You have just created a square using just a straightedge and a compass.

The figure below shows the square in light orange.

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