Here is how to construct a square using a straightedge, a compass, and also of food a pen or a pencil.

You are watching: How to construct a square using a compass

Step 1

Draw a segment and call it AB.


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Step 2

Construct a heat perpendicular to segment abdominal and let i be the point where the perpendicular heat intersects segment AB. Review the lesson about constructing perpendiculars if needed. 


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Step 3

Set her compass to the length of IB. Then, copy segment IB ~ above the perpendicular heat (shown with the blue line). Brand the brand-new point ~ above the perpendicular line C.


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Step 4

Set her compass again to the length of IB and draw arcs from point C and also from suggest B. Label the point of intersection in between the two new arcs D.


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Step 5

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


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How to build a square : an approach #2 

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


Step #2: Using a compass, measure up the size of segment AB. Keeping the opened of your compass the same, placed the needle of the compass at allude A and draw a circle. The size of the radius the the circle will be equal to the size of segment AB. 

Then, still keeping the opened of her compass the same, placed the needle the the compass at point B and also draw an additional circle. ~ you space done drawing both circles, girlfriend should finish up with the number below. Finally, brand the suggest where the two circles satisfy I. 


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


Step #6: Finally, affix 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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