Question

What are the steps for using a compass and straightedge to construct a square?

Answer 1

For problems of this type, you need to look at the steps that only require elements that are already known. If a step requires something that hasn't been done yet. THEN THAT STEP COMES LATER. So looking at the 7 available steps, only the step "Construct horizontal PQ" is possible since that's just a matter of drawing a straight line and labeling the end points P and Q. In any case, here are the 7 steps in order. The number in parenthesis after the 1st number is the original scrambled order of that step.  
1(2). Construct horizontal PQ 
2(5). Construct a circle with point P as the center and a circle with point Q as a center, each circle having radius PQ 
3(4). Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S 
4(6). Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T
 5(1). Construct a circle with point T as the center with radius TQ 
6(7). Label the point of intersection of circle T and RS closest to point R, point
U, and the point of intersection of circle T and RS closest to point S, point V. 
7(3). Construct PU, UQ, QV, and VP to complete square PUQV.

Answer 2

Answer:

1) Construct horizontal PQ  

2) Construct a circle with point P as the center and a circle with point Q as a center, each circle having radius PQ  

3) Label the point of intersection of the two circles above PQ, point R, and the point of intersection of the two circles below PQ, point S  

4) Construct RS, the perpendicular bisector of PQ, intersecting PQ at point T

5) Construct a circle with point T as the center with radius TQ  

6) Label the point of intersection of circle T and RS closest to point R, point

U, and the point of intersection of circle T and RS closest to point S, point V.  

7) Construct PU, UQ, QV, and VP to complete square PUQV.

Step-by-step explanation:

Just took the test, hope this helps :)