Question

What are the steps for using a compass and straightedge to construct a square? Drag the steps and drop them in order from start to finish.
(A) construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ .

(B) Construct horizontal ​ HJ¯¯¯¯¯ ​

(C) Construct a circle with point M as the center with radius MJ .

(D) Label the point of intersection of the two circles above​ ​ HJ¯¯¯¯¯ ​​, point K, and the point of intersection of the two circles below ​ HJ¯¯¯¯¯ ​, point L.

(E) Construct KL¯¯¯¯¯ , the perpendicular bisector of ​ HJ¯¯¯¯¯ ​, intersecting​ ​ HJ¯¯¯¯¯ ​ ​​at point M.

(F) Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .Label the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point K, point N, and the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point L, point O.

Answer 1

The steps for using a compass and straightedge to construct a square are as following:

1) Construct a circle with point H as the center and a circle with point J as a center with each circle having radius HJ.

2) Construct horizontal HJ¯¯¯¯¯ ​

3) Label the point of intersection of the two circles above​ ​ HJ¯¯¯¯¯ ​​, point K, and the point of intersection of the two circles below ​ HJ¯¯¯¯¯ ​, point L.

4) Construct KL¯¯¯¯¯ , the perpendicular bisector of ​ HJ¯¯¯¯¯ ​, intersecting​ ​ HJ¯¯¯¯¯ ​ ​​at point M.

5) Construct a circle with point M as the center with radius MJ.

6) Label the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point K, point N, and the point of intersection of circle M and ​ KL¯¯¯¯¯ ​ closest to point L, point O.

7) Construct HN¯¯¯¯¯¯ , NJ¯¯¯¯¯ , JO¯¯¯¯¯ , and OH¯¯¯¯¯¯ to complete square HNJO .